diff --git a/experiments/learnability/train_policy_only_gold/driver.log b/experiments/learnability/train_policy_only_gold/driver.log new file mode 100644 index 0000000000000000000000000000000000000000..10c8b3e10d6df100b82734670e481ca5d5110dee --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/driver.log @@ -0,0 +1,49 @@ +[2026-06-29 07:09:14] ===== START: 10 policy-only GOLD jobs on GPUs 1 2 3 ===== +[2026-06-29 07:09:14] --- Phase 1: training (policy-only gold) --- +[2026-06-29 07:09:14] TRAIN [0/10] gold_0pt/s42 (seed=42) -> gpu 1 +[2026-06-29 07:09:14] TRAIN [1/10] gold_0pt/s43 (seed=43) -> gpu 2 +[2026-06-29 07:09:14] TRAIN [2/10] gold_0pt/s44 (seed=44) -> gpu 3 +[2026-06-29 07:09:24] TRAIN DONE gold_0pt/s42 +[2026-06-29 07:09:25] TRAIN DONE gold_0pt/s43 +[2026-06-29 07:09:25] TRAIN DONE gold_0pt/s44 +[2026-06-29 07:09:25] TRAIN [3/10] gold_0pt/s45 (seed=45) -> gpu 1 +[2026-06-29 07:09:25] TRAIN [4/10] gold_0pt/s46 (seed=46) -> gpu 2 +[2026-06-29 07:09:25] TRAIN [5/10] gold_1pt/s42 (seed=42) -> gpu 3 +[2026-06-29 07:09:35] TRAIN DONE gold_0pt/s46 +[2026-06-29 07:09:35] TRAIN DONE gold_0pt/s45 +[2026-06-29 07:09:41] TRAIN DONE gold_1pt/s42 +[2026-06-29 07:09:41] TRAIN [6/10] gold_1pt/s43 (seed=43) -> gpu 1 +[2026-06-29 07:09:41] TRAIN [7/10] gold_1pt/s44 (seed=44) -> gpu 2 +[2026-06-29 07:09:41] TRAIN [8/10] gold_1pt/s45 (seed=45) -> gpu 3 +[2026-06-29 07:10:03] TRAIN DONE gold_1pt/s43 +[2026-06-29 07:10:03] TRAIN DONE gold_1pt/s44 +[2026-06-29 07:10:03] TRAIN DONE gold_1pt/s45 +[2026-06-29 07:10:03] TRAIN [9/10] gold_1pt/s46 (seed=46) -> gpu 1 +[2026-06-29 07:10:20] TRAIN DONE gold_1pt/s46 +[2026-06-29 07:10:20] --- Phase 1 complete --- +[2026-06-29 07:10:20] --- Eval phase (final, epoch_2.pt, value-free rollout) --- +[2026-06-29 07:10:20] EVAL-final [0] gold_0pt/s42 (epoch_2.pt) -> gpu 1 +[2026-06-29 07:10:20] EVAL-final [1] gold_0pt/s43 (epoch_2.pt) -> gpu 2 +[2026-06-29 07:10:20] EVAL-final [2] gold_0pt/s44 (epoch_2.pt) -> gpu 3 +[2026-06-29 09:34:20] EVAL-final DONE gold_0pt/s42 +[2026-06-29 09:35:40] EVAL-final DONE gold_0pt/s43 +[2026-06-29 09:41:03] EVAL-final DONE gold_0pt/s44 +[2026-06-29 09:41:03] EVAL-final [3] gold_0pt/s45 (epoch_2.pt) -> gpu 1 +[2026-06-29 09:41:03] EVAL-final [4] gold_0pt/s46 (epoch_2.pt) -> gpu 2 +[2026-06-29 09:41:03] EVAL-final [5] gold_1pt/s42 (epoch_2.pt) -> gpu 3 +[2026-06-29 11:05:33] EVAL-final DONE gold_1pt/s42 +[2026-06-29 12:12:37] EVAL-final DONE gold_0pt/s45 +[2026-06-29 12:19:12] EVAL-final DONE gold_0pt/s46 +[2026-06-29 12:19:12] EVAL-final [6] gold_1pt/s43 (epoch_2.pt) -> gpu 1 +[2026-06-29 12:19:12] EVAL-final [7] gold_1pt/s44 (epoch_2.pt) -> gpu 2 +[2026-06-29 12:19:12] EVAL-final [8] gold_1pt/s45 (epoch_2.pt) -> gpu 3 +[2026-06-29 13:44:59] EVAL-final DONE gold_1pt/s45 +[2026-06-29 13:52:17] EVAL-final DONE gold_1pt/s43 +[2026-06-29 13:57:03] EVAL-final DONE gold_1pt/s44 +[2026-06-29 13:57:03] EVAL-final [9] gold_1pt/s46 (epoch_2.pt) -> gpu 1 +[2026-06-29 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'P -> false])))))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 iff_i@type goal4 iff_i).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]].", + "c x0", + "=> (x0 p2@type p3@type p2).", + "c em", + "=> (em goal19).", + "c x0", + "=> (x0 p2@type goal7 p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 430, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a or_il", + "=> .", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x1", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6512, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ['A -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ['A -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false].", + "a p4", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [[('P : 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prop) -> 'P -> (or 'P 'Q)])) (not (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]) (not (or (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> 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'P -> 'Q -> (and 'P 'Q)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em 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(not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 39, + "evals_used": 1237, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ['A -> 'A]]); [('A : prop) -> ['A -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> (or 'P (not 'P))] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> (or 'P (not 'P))] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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[[('P : prop) -> (or 'P (not 'P))] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L0_1" + }, + { + "solved": true, + "greedy_solved": true, + "n_traces": 1, + "evals_used": 18, + "solution_actions": [ + "intro.", + "intro.", + "intro.", + "c and_er", + "=> (and_er x x0 x1).", + "c and_el", + "=> (and_el x x0 x1)." + ], + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": true, + "outcome": "solved", + "depth_used": 7, + "evals_used": 18, + "actions": [ + "intro.", + "intro.", + "intro.", + "c and_er", + "=> (and_er x x0 x1).", + "c and_el", + "=> (and_el x x0 x1)." + ] + } + ], + "problem": "extrinsic_L0_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 21490, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 644, + "actions": [ + "intro.", + 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prop) -> (and x 'B) -> 'B]]]) -> false].", + "a or_e", + "=> [x -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] -> false]]; [(not x) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] -> false]].", + "c em", + "=> (em goal4).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]) -> false].", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]]))).", + "a not_i", + "=> [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]])) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]] -> [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]])) -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]) -> [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]])) -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]] -> [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]])) -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) 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false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not x0)); (not x0).", + "a exfalso", + "=> false.", + "a x3", + "=> .", + "c x3", + "=> (x3 not_i).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 404, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + 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-> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))) -> false].", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])].", + "intro.", + "c x", + "=> (x goal or_e@type and_er).", + "c x", + "=> (x iff_i@type not_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2189, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal15 and_er).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso and_er).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p3@type p1 p3).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> 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false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4654, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a 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(not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x", + "=> (x p@type@2 p1@type p1).", + "c x", + "=> (x p1@type@2 or_e@type or_e).", + "a exfalso", + "=> false.", + "c x", + "=> (x p2@type iff_er@type iff_er).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false.", + "c x", + "=> (x not_e@type p9@type p9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2666, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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-> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])].", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> 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-> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 956, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type and_er@type p0 and_er).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type and_er@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> 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-> ('B : prop) -> 'A -> (or 'A 'B)] -> false]); [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1545, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x goal 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-> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6398, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) 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['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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[false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (or x 'B)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> (or x 'B)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a x1", + 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goal11).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2052, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type goal5 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> 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'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> 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['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal6).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x", + "=> (or (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> (or [('P 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (or (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]]].", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]])); (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]] -> (not (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]))]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]) -> (not (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]]))].", + "c em", + "=> (em goal6).", + "c em", + "=> (em goal).", + "c em", + "=> (em goal5).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal1).", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a or_e", + "=> [x -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not x) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a or_e", + "=> [x -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not x) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a or_e", + "=> [x -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not x) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 407, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "c x", + "=> (x and_i).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c not_e", + "=> (not_e or_e@type p5 or_e).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10559, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('A : prop) -> (not 'A) -> 'A -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_il", + "=> [('A : prop) -> (not 'A) -> 'A -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> (not 'A) -> 'A -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not 'A) -> 'A -> false]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_ir", + "=> (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em goal1).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('A : prop) -> (not 'A) -> 'A -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em goal9).", + "a or_il", + "=> .", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x0", + "=> (x0 and_i@type exfalso@type x0 exfalso).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] 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p1).", + "c and_el", + "=> (and_el p@type or_ir@type p3).", + "a x2", + "=> (iff false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c p4", + "=> (p4 x0 p3@type p3).", + "c p4", + "=> (p4 p2@type@2 exfalso@type exfalso).", + "c x1", + "=> (x1 p2@type goal p2 not_e).", + "c em", + "=> (em em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 395, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> (not 'A) -> 'A -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> (not 'A) -> 'A -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em false).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 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'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c x0", + "=> (x0 or_e@type goal14 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p1@type p1@type p1).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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(iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 47, + "evals_used": 5643, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not x) -> x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not x) -> x -> false]].", + "intro.", + 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'P -> (or 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))])].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)].", + "a x", + "=> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) 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'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": true, + "outcome": "solved", + "depth_used": 5, + "evals_used": 27, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> ." + ] + } + ], + "problem": "extrinsic_L0_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 28586, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 179, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> 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'P 'Q)] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) (not (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])))).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em 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"intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a x", + "=> (or (or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a 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[[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 iff_i).", + "c x1", + "=> (x1 exfalso@type 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"=> (x0 and_er@type not_e@type and_er not_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3391, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p1@type not_e p1).", + "c and_el", + "=> (and_el not_e@type p1@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]].", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso em).", + "c em", + "=> (em goal4).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 429, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a 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false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c em", + "=> (em goal9).", + "intro.", + "intro.", + "intro.", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 786, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p4@type@2).", + "c em", + "=> (em goal2).", + "c x", + "=> (x p3@type@2).", + "c x", + "=> (x p7@type@2).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p10@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p11@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 507, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not [('A : prop) -> (or 'A (not 'A))]) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (or 'A (not 'A))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]); [[('A : prop) -> (or 'A (not 'A))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "a not_i", + "=> [[[('A : prop) -> (or 'A (not 'A))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]] -> false].", + "c em", + "=> (em p3@type)." + ] + } + ], + "problem": "extrinsic_L0_12" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 25950, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 293, + "actions": [ + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 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-> 'Q -> (or 'P 'Q)] (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> .", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]); [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> false].", + "c em", + "=> (em p@type).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal4).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not 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not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[x -> false] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em p1@type@2).", + "c x2", + 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prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c x0", + "=> (x0 p3@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal15).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 351, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P]))]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P]))].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))))) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C])]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))))) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C])].", + "a x", + "=> (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]); [(or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p0@type).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal8).", + "a x", + "=> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); [(or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) -> false]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a x", + "=> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); [(or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) -> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]; [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (or (or (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 551, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em iff_i@type).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)])).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c not_e", + "=> (not_e or_e@type x2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a not_e", + "=> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))); (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)])).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)])))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]]).", + "c em", + "=> (em goal21).", + "a x0", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]))))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 324, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[false -> ('P : prop) -> 'P] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> false])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x", + "=> false.", + "c em", + "=> (em p4@type).", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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(and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('A : prop) -> 'A -> (not (not 'A))] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2258, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> 'A -> (not (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> 'A -> (not (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 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-> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 633, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [false -> [('P : prop) -> ('Q : prop) -> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c 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(not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2132, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]); [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> 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: prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or false (not false)) -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or false (not false)) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or false (not false)) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8695, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_e@type not_i or_e).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_e@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er 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false] (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P]))]; [(or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])) -> (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P]))].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])))]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [(or [(not [false -> ('P : prop) -> 'P]) -> false] (not [false -> ('P : prop) -> 'P])) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3540, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x1", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "c x3", + "=> (x3 goal6 p1@type p1).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "a x0", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x0", + "=> false.", + "c x3", + "=> (x3 p7@type@2 p4@type p4).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 goal p0@type p0).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "intro.", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a x", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> (iff [('P : prop) -> (or 'P (not 'P))] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 38, + "evals_used": 2035, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P 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-> 'P -> false])))]] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])]].", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]] -> (and (not (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 450, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> 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(or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)); (iff [('P : prop) -> ('Q 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]." + ] + } + ], + "problem": "extrinsic_L2_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 14672, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a 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false])])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])); (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]).", + "a x0", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]].", + "a x0", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]]).", + "c em", + "=> (em goal18).", + "a x0", + "=> (and (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]] (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]])) (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 492, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> 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-> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 880, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P 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-> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))]; [(not [false -> ('P : prop) -> 'P]) -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6972, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] false); [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> [false -> [false -> false]]]; [false -> [false -> [false -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]].", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]]; [(not false) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + 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and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2407, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 680, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])).", + "a x0", + "=> (and (not [('P : prop) -> (or 'P (not 'P))]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false false).", + "a x0", + "=> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (and false false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (and false false))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (and false false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ('R 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false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1339, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> 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'P] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])]]] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", 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(and 'C 'B)]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and 'C x) -> (and 'C 'B)]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal2).", + "c em", + "=> (em goal).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", 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false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type or_e@type or_e).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))); (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not (not (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))))].", + 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])])].", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])]].", + "a x", + "=> (and (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c em", + "=> (em p@type@2).", + "c x0", + "=> (x0 iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", 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false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2039, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and 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not_e", + "=> (not_e em@type x1 em).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4272, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "c x2", + "=> (x2 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[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 599, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]; false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> 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p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> (iff (and 'A 'A) 'A)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])]; [[('A : prop) -> (iff (and 'A 'A) 'A)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6730, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> 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-> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 310, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a x1", + "=> (iff (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; 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prop) -> (and 'P 'Q) -> 'P])].", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))); [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> false].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1760, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 not_i@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(iff (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ['P -> false] -> (not 'P)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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'Q]))))) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_el@type p8@type p8).", + "c x", + "=> (x and_el@type p13@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 571, + "actions": [ + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c em", + "=> (em iff_el@type).", + "c x0", + "=> (x0 iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 goal0@1).", + "c x0", + "=> (x0 exfalso@type).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "c em", + "=> (em goal17)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 656, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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(iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_ir", + "=> .", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> false.", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)]]; [[[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)] -> [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])]; [(not [false -> ('P : prop) -> 'P]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)])].", + "a x3", + "=> (iff (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[false -> ('P : prop) -> 'P] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) false)]) [false -> ('P : prop) -> 'P]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 460, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type@2).", + "c em", + "=> (em p3@type).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 970, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false].", + "c x0", + "=> (x0 not_e@type p3@type@2 not_e).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal11).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1039, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 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'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7307, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff 'A 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 307, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a iff_i", + "=> [x -> x]; [x -> x].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 524, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [false -> false]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p8@type@2).", + "c em", + "=> (em or_ir@type)." 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exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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: prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]))); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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-> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p@type).", + "c 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false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a x0", + "=> (and (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [(not 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(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 501, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "c em", + "=> (em goal).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (not [('P : prop) -> (not 'P) -> 'P -> 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-> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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+ "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] false); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] false)]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] false)].", + "c x0", + "=> (x0 or_ir@type goal2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] 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-> (iff x 'C)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type 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false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11632, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_il", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q 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false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 4500, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 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(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] 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'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5852, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]); [false -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or false [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x0", + "=> false.", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) (or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) -> false]; [(or (or false [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p12@type p3 p12).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2409, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P 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: prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_ir@type p2@type@2 or_ir).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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-> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x", + "=> (x iff_i@type p0@type p0).", + "c x", + "=> (x not_e@type and_i@type and_i).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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prop) -> 'P -> (or 'P 'Q)]))))].", + "intro.", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> (not (not x))])); (not [[('P : prop) -> (or 'P (not 'P))] -> (not (not x))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 627, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q 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-> 'Q]) -> false].", + "intro.", + "c em", + "=> (em p3@type).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 628, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : 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(and (iff (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]]))] (not [('P : prop) -> (not 'P) -> 'P -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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false]])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal12).", + "c em", + "=> (em p4@type@2).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 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+ ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7241, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x0", + "=> (x0 iff_el@type or_ir@type or_ir).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 p@type and_er@type and_er).", + "c x0", + "=> (x0 p@type or_il@type or_il).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])].", + "c x0", + "=> (x0 iff_i@type and_el@type and_el)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and x [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> x; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "intro.", + "intro.", + "intro.", + "c em", + "=> (em x0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x0 -> false]; [(not x0) -> false].", + "a x3", + "=> (iff x0 false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff x0 false)].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]].", + "c em", + "=> (em p1@type).", + "a x3", + "=> (iff [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]).", + "a iff_i", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)] -> [false -> ('P : prop) -> 'P]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]].", + "a x3", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]])].", + "a x3", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]])).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]))]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x0 false)]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [x0 -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not x0) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 46, + "evals_used": 4440, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]); [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]) (not 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[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]) -> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]) (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 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'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 iff_el@type iff_el@type iff_el).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 p@type iff_i@type iff_i).", + "c x0", + "=> (x0 p@type iff_er@type iff_er).", + "a x", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (not [('P : prop) -> (or 'P (not 'P))]) (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or (not [('P : prop) -> (or 'P (not 'P))]) (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "c x0", + "=> (x0 iff_i@type or_e@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 631, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> 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-> 'R] -> 'R] -> (not (not (not x)))]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not (not x)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x0", + "=> (x0 p4@type@2 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p2@type p2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_er@type and_er).", + "a or_e", + "=> [(not (not x)) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (not (not x))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 447, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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-> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a x0", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2713, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : 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[[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]].", + "intro.", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] -> false]].", + "c em" + ] + }, + { + "mode": "sample", + 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-> 'P] (not [false -> ('P : prop) -> 'P]))) (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))))).", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (or (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))))]; [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> (not (or (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5109, + 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x2", + "=> (x2 p5@type@2 p6@type p6).", + "c x2", + "=> (x2 goal7 em@type em).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 380, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1332, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 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-> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + 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exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not false))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not false)))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 498, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P 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+ "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))])].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 969, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c x1", + "=> (x1 iff_i@type iff_el@type x2 iff_el).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 950, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + 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false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> 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'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type iff_i@type p1).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a p4", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a p4", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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-> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1856, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 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(not 'P)] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (and [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 325, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x2", + "=> .", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 600, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (not (or x 'B)) -> (and (not x) (not 'B))]]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "intro.", + "c x1", + "=> (x1 iff_er).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 460, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[false -> ('P : prop) -> 'P] -> 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false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> 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exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 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'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false] -> false]; [(not [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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: prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [false -> [false -> false]]]; 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false.", + "c em", + "=> (em iff_el@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em or_il@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1872, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a 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"=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 643, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]].", + 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]; [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or false [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]); [false -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 362, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 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[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> false].", + "c x", + "=> (x p@type and_el@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not false) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "a or_e", + "=> [false -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]]; [(not false) -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [false -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]]]; [(not [false -> ('P : prop) -> 'P]) -> [false -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 x2 or_ir@type).", + "c x0", + "=> (x0 x2 p0@type).", + "c em", + "=> (em or_e@type).", + "a x1", + "=> .", + "intro.", + "intro.", + "c em", + "=> (em goal0).", + "a x1", + "=> false.", + "a or_e", + "=> [[false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]] -> false]; [(not [false -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 x1).", + "c em", + "=> (em not_i@type).", + "a x1", + "=> .", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em or_il@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : 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not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c 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-> (or 'P (not 'P))] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]].", + "c em", + "=> (em p2@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 709, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 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(and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not false)]; [[('P : prop) -> (or 'P (not 'P))] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] [('P : prop) -> (or 'P (not 'P))]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [false -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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[false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]]; 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false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "c em", + "=> (em em@type).", + "a x0", + "=> (iff (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a iff_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a x", + "=> (iff (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false].", + "intro.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]); [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false].", + "c x", + "=> (x or_e@type p3@type@2 p3).", + "c x", + "=> (x not_e@type p@type@2 p).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]; [(not [('A : prop) -> ('B : prop) 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false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c x2", + "=> (x2 p0@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> false].", + "intro.", + "c x2", + "=> (x2 p0@type@2).", + "c x3" + ] + }, + { + "mode": "sample", + 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "c x1", + "=> (x1 goal8).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 486, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]; [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a x0", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 439, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 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'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]))).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not 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false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2040, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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-> 'R] -> 'R] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])) false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 617, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) 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(not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x0", + "=> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) 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+ "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1015, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c x4", + "=> (x4 p2@type iff_i@type x1).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 582, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", 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p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 439, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]].", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 x).", + "c x", + "=> (x goal goal false x0 x0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; 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-> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 316, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [('P : prop) -> 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-> (and 'P 'Q)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (iff (not 'A) ['A -> false])] -> false]; [(not [('A : prop) -> (iff (not 'A) ['A -> false])]) -> false].", + "intro.", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> (iff (not 'A) ['A -> false])] (not [('A : prop) -> (iff (not 'A) ['A -> false])]))).", + "c x", + "=> (x p1@type@2)." + ] + } + ], + "problem": "extrinsic_L3_14" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 10, + "evals_used": 20930, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 741, + "actions": [ + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not false) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 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exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1466, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a 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-> false].", + "c x0", + "=> (x0 em@type goal4).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type 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('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1614, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x p@type goal15 p).", + "c em", + "=> (em or_ir@type).", + "intro.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]])); (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]]).", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 14852, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and x (or x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and x (or x 'B)) x)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a iff_i", + "=> [(and x (or x x2)) -> x]; [x -> (and x (or x x2))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p@type p2@type p2).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir x1).", + "c x1", + "=> (x1 not_i@type p5@type not_i p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false iff_el@type iff_el).", + "c x1", + "=> (x1 and_er@type p11@type and_er p11).", + "c p9", + "=> (p9 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4@1@2).", + "c p4", + "=> (p4 x p1@type p1).", + "c p4", + "=> (p4 p1@type p@type p).", + "c p9", + "=> (p9 p8@type and_i@type p8 x1).", + "c p9", + "=> (p9 p17@type p17@type p17 p17).", + "c p4", + "=> (p4 or_ir@type p5@type p5).", + "c and_er", + "=> (and_er and_er@type p11@type p14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> 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'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> 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: prop) -> (not 'P) -> 'P -> false] (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0", + "=> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false)))]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 530, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", 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(em x).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]) -> false].", + "a or_e", + "=> [false -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> false]]; [(not false) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]] -> [false -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] -> false]]]; [(not [[('A : prop) -> ('B : prop) -> (iff (and 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'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "c em", + "=> (em exfalso@type).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [false -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> (not (not (not 'A))) -> (not 'A)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> (not (not (not 'A))) -> (not 'A)])].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])).", + "a x", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p0@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (or [('A : prop) -> (not (not (not 'A))) -> (not 'A)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 40, + "evals_used": 2313, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type or_e@type not_e or_e).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 or_e@type or_il@type or_e or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : 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-> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "c em", + "=> (em p5@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1945, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> 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-> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x2", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])) -> false] (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]))).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[false -> ('P : prop) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[false -> ('P : prop) -> 'P] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> 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false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1889, + "actions": [ + 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c x", + "=> (x p1@type p1@type p1).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 542, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and (or (not [('P 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: prop) -> (not 'P) -> 'P -> false] false)))].", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p0@type@2).", + "intro.", + "a x0", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false)))).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a x0", + "=> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))]].", + "a x0", + "=> (and (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))]]).", + "c em", + "=> (em goal23).", + "a x0", + "=> (and (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P])) (and (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) (and [('P : prop) -> (or 'P (not 'P))] (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)] (and [('P : prop) -> (not 'P) -> 'P -> false] false))))] (not [false -> ('P : prop) -> 'P]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c em", + "=> (em p@type@2).", + "c x0", + "=> (x0 iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em" + ] + }, + { + "mode": "sample", 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-> false]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]).", + "a x0", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]] (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) false).", + "a x0", + "=> (and (not (not [false -> ('P : prop) -> 'P])) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) false)).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (and (not (not [false -> ('P : prop) -> 'P])) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) false))]; [(not (not [false -> ('P : prop) -> 'P])) -> (and (not (not [false -> ('P : prop) -> 'P])) (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1763, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x1", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x1", + "=> (iff false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x2", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]] -> false].", + "c em", + "=> (em goal8).", + "a or_il", + "=> .", + "a x1", + "=> (iff false (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a iff_i", + "=> [false -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [false -> ('P : prop) -> 'P]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 375, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + 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false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x 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"a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e p@type x1 p).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a not_i" + ] + }, + { + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + 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'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]]; [(not [('P : prop) -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])) (not [[('P : prop) -> ('Q : prop) -> 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 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prop) -> ['P -> false] -> (not 'P)]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P 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'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a x2", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]).", + "c em", + "=> (em goal22).", + "a x2", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]])) (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (or 'P (not 'P))] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : 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-> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])].", + "c em", + "=> (em p6@type).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> false])].", + "a p4", + "=> (or 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: prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or x (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [false -> ('P : prop) -> 'P]) -> (or x (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a x0", + "=> (or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] [[false -> ('P : prop) -> 'P] -> (or x [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]); [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] -> [[false -> ('P : prop) -> 'P] -> (or x (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [[[false -> ('P : prop) -> 'P] -> (or x [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] -> [[false -> ('P : prop) -> 'P] -> (or x (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "c em", + "=> (em goal14).", + "a or_il", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_ir", + "=> .", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a x1", + "=> false.", + "a x0", + "=> (or (not false) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]); [(not false) -> false]; [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] -> false].", + "a x1", + "=> false." + ] 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false]) -> false].", + "intro.", + "a x2", + "=> .", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4947, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P 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prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 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(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]] -> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 619, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not [('P 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false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 620, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> 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('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]; [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] -> false].", + "a or_il", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "c em", + "=> (em or_ir@type).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x1", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "a or_ir" + ] + }, + { + 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[('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x1", + "=> (x1 p4@type).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 and_i).", + "c x1", + "=> (x1 p1@type).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : 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'P 'Q) -> 'P]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c em", + "=> (em p@type@2).", + "c x0", + "=> (x0 iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 iff_i).", + "a exfalso", + "=> false.", + "a x0", + "=> .", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 736, + 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false]) (and (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]))) (and (not (not [false -> ('P : prop) -> 'P])) (or (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]) (and (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false])))))).", + "a exfalso", + "=> false.", + "a x0", + "=> (or (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]) false) (and 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false.", + "a not_e", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal13@2@1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 363, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e p0@type x1 p0).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> 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prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x2", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x2", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a x1", + "=> (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> (and (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (and (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]].", + "a x2", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]] (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x2", + "=> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]] (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a x2", + "=> (and (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]]] (iff (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal19).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 400, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (or (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) [[false -> ('P : prop) -> 'P] -> false]) (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) [[false -> ('P : prop) -> 'P] -> false])).", + "a or_il", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) [[false -> ('P : prop) -> 'P] -> false]).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 550, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]; [(not false) -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]].", + "a or_e", + "=> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]; [(not false) -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [(not false) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not false)) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type@2).", + "c em", + "=> 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x", + "=> (or false (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))); [false -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x", + "=> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> (iff 'A (not 'A)) -> false])]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> (iff 'A (not 'A)) -> false])]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e" + ] + }, + { + "mode": "sample", + 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(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x0", + "=> (x0 exfalso@type and_er@type exfalso and_er).", + "c and_er", + "=> (and_er exfalso@type and_er@type p7)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + 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: prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2232, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A (not 'A)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff 'A (not 'A)) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12557, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(iff x (not x)) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(iff x (not x)) -> false]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c iff_er", + "=> (iff_er x x2@type@2 x2).", + "c iff_el", + "=> (iff_el x x2@type@2 x2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 iff_i@type p1@type iff_i p1).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso or_il).", + "c p9", + "=> (p9 exfalso@type not_e@type exfalso not_e).", + "c x1", + "=> (x1 and_i@type and_i@type p9 and_i).", + "c x0", + "=> (x0 exfalso@type not_e@type exfalso not_e).", + "a exfalso", + "=> false.", + "c p9", + "=> (p9 or_il@type not_e@type or_il not_e).", + "c em", + "=> (em x2@type@2).", + "c x1", + "=> (x1 iff_er@type p12@type iff_er p14).", + "c x1", + "=> (x1 p0@type exfalso@type p0 exfalso).", + "c p9", + "=> (p9 p7@type p11@type p7 p11).", + "c p9", + "=> (p9 p17@type p15@type p17 p15).", + "c x1", + "=> (x1 and_el@type p5@type and_el p5)." + ] + } + ], + "problem": "extrinsic_L3_24" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 8, + "evals_used": 12125, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 375, + "actions": [ + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> (not (not (or 'A (not 'A))))]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('A : prop) -> (not (not (or 'A 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-> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 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exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 619, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 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['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "a x3", + "=> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]].", + "a x3", + "=> (or (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0))) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0)))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0)))]))); [(or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0))) -> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0)))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (or x0 (not x0)))])) -> (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not [('P : prop) -> (not 'P) -> 'P -> false]))]." + ] + } + ], + "problem": "extrinsic_L3_25" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 17218, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 458, + "actions": [ + "intro.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em x).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "a or_e", + "=> [x -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]]; [(not x) -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [x -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]]]; [(not [false -> ('P : prop) -> 'P]) -> [x -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]]].", + "a or_e", + "=> [x -> [[false -> ('P : prop) -> 'P] -> [x -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]]]]; [(not x) -> [[false -> ('P : prop) -> 'P] -> [x -> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> ('C : 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prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false]].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false]]]].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em goal5).", + "a or_e", + "=> 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(not 'P)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 507, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not x) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + 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prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] false); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] false)]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] false)].", + "c x0", + "=> (x0 or_ir@type goal2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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-> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]); [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]])].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not x); x.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal11).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2415, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; 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-> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x", + "=> (x goal x3 x1).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 503, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]].", + "a or_e", + "=> [x -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]; [(not x) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [x -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not [false -> ('P : prop) -> 'P]) -> [x -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6801, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + 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-> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "c em", + "=> (em x).", + "c em", + "=> (em x1@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (not x)) -> (not (not x0))]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (not x)) -> (not (not x0))]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", + "c x4", + "=> (x4 not_i@type p1@type@2 not_i).", + "c x3", + "=> (x3 p2@type goal3 p2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [(or (not (not [x -> x0])) (not (not (not [x -> x0])))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (not x)) -> (not (not x0))]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "c em", + "=> (em not_e@type).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or 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p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]]].", + "a x", + "=> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> false] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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[false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 510, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal3).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + 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[('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or false [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false]); [false -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or false [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false])]; [(or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> (or false [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])] -> false])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 711, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 30, + "evals_used": 115, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : 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(not (not [('P : prop) -> (not 'P) -> 'P -> false]))) [('P : prop) -> (or 'P (not 'P))]) -> (or (not x) (iff x (not (not x))))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not x) (iff x (not (not x))))].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_ir", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 603, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [x -> (not (not x))]; [(not (not x)) -> x].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [x -> (not (not x))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]]].", + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (iff [x -> (not (not x))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 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[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not false)]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not false)]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A (not (not 'A)))]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> (not (not x0))]; [(not (not x0)) -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 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prop) -> (not 'P) -> 'P -> false] -> [x0 -> (not (not x0))]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[x0 -> (not (not x0))] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x3", + "=> (x3 x1).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1386, + 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'P] -> (iff 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4245, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> [(not (not 'A)) -> 'A]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> [(not (not 'A)) -> 'A]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> [(not (not 'A)) -> 'A]]); [('A : prop) -> [(not (not 'A)) -> 'A]].", + "c em", + "=> (em 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 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+ "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or 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exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5852, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "c x0", + "=> (x0 p@type and_er@type and_er).", + "c x0", + "=> (x0 p@type or_il@type or_il).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (or (not [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [(not [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x0", + "=> (x0 exfalso@type p1@type p1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not x) -> 'B] -> 'B]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 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'B] -> [(not 'A) -> 'B] -> 'B]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L4_3" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24198, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 689, + "actions": [ + "c em", + "=> (em or_e@type).", + "c em", + 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or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]) -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]].", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 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-> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]]; [(not [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]) -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]); [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal8).", + "c em", + "=> (em goal2).", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]] -> false].", + "c em", + "=> (em goal14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1257, + "actions": [ + "c em", + "=> (em or_il@type).", + "intro.", + "intro.", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p2@type).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_ir@type).", + "intro.", + "c em", + "=> (em goal17).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em 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prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]) -> false].", + "c x", + "=> (x p1@type iff_el@type iff_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el 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['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[false -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]]; [(not [false -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]) -> false].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> false]]; [(not [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false]) -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> false]].", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> false]]]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false] -> false]]].", + "c em", + "=> (em goal16).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 675, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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-> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> 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-> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]); [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] 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prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p12@type p3 p12).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1379, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + 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-> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5175, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + 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'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [('P : prop) -> (or 'P (not 'P))]); [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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-> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 2080, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 iff_i@type or_e@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il" + ] + } + ], + "problem": "extrinsic_L4_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 19566, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 166, + "actions": [ 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'P]] -> false]) -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not false))]))].", + "intro.", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not false))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 579, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a and_i", + "=> false.", + "a x", + "=> (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x", + "=> (and (and false (and false [('P : prop) -> ('Q : prop) 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(and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a x", + "=> (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a x", + "=> (and (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> (and (and (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not (or (not [('P : prop) -> ('Q : 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (not 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(and_er not_i@type em@type p5).", + "a p7", + "=> (or (or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])) [false -> ('P : prop) -> 'P]); [(or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a p4", + "=> .", + "c p13", + "=> (p13 p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 449, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> false]; [(not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 546, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "c em", + "=> (em goal5).", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p8@type@2).", + "c em", 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false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false].", + "a x", 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or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2235, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 10720, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", 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"a x", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and false false)]).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and false false)])]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and false false)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and 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-> 'Q]]) -> (and false false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and false false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c x2", + "=> (x2 x1).", + "c not_e", + "=> (not_e or_il@type p4 or_il).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 679, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (or x [x -> 'B])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a x0", + "=> (and x (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and x (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false)).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 433, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x [x -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type@2).", + "a or_e", + "=> [[('P : 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[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + 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['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2003, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 660, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x [x -> 'B])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x [x -> 'B])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not x); x.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]); [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 542, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "a exfalso", + "=> false.", + "c em", + 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prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 422, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 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false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em exfalso@type).", + "a x", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em goal5).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]] -> false]; [(not [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 916, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e or_e@type x or_e).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x", + "=> (x iff_i@type p5@type iff_i p5)." + ] + } + ], + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 22606, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 375, + "actions": [ + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", 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(not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 482, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not false))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", 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-> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 396, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "a not_i", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false].", + "intro.", + "a x", + "=> (not [false -> (not false)]).", + "a not_i", + "=> [[false -> (not false)] -> false].", + "a x", + "=> (not [[[false -> (not false)] -> false] -> (not [[false -> (not false)] -> false])]).", + "a x", + "=> (not [(not [[[false -> (not false)] -> false] -> (not [[false -> (not false)] -> false])]) -> (not (not [[[false -> (not false)] -> false] -> (not [[false -> (not false)] -> false])]))]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> (not false)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a x", + "=> (not [false -> (not false)]).", + "c em", + "=> (em goal4).", + "a x", + "=> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]).", + "c em", + "=> (em p0@type).", + "a x", + "=> (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]).", + "a x", + "=> (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]).", + "a x", + "=> (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]).", + "a x", + "=> (not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]).", + "a x", + "=> (not [(not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]))]).", + "a not_i", + "=> [[(not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]))] -> false].", + "a x", + "=> (not [[[(not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]))] -> false] -> 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false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]) -> (not (not [(not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]) -> (not (not [(not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]) -> (not (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))]))]))]))]))] -> false])]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> (not false)]).", + "c em", + "=> (em goal12@1).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> (not false)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [false -> (not false)])].", + "intro.", + "a x", + "=> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]).", + "c x0", + "=> (x0 and_er@type).", + "c x0", + "=> (x0 or_il@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]]].", + "c em", + "=> (em p5@type@2).", + "a 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'P) -> 'P -> false])]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) 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prop) -> 'P] -> false]].", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "a x", + "=> (or [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x", + "=> (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> (or [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 380, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 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[[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not false); false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x0", + "=> (x0 iff_i@type or_e@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10525, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + 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(iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2417, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [false -> ('P : prop) -> 'P])]); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [false -> ('P : prop) -> 'P])] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 p@type p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q 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'Q) -> 'Q]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "a x", + "=> (or false (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))); [false -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] 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-> ['Q -> 'P]] -> false]).", + "a x0", + "=> (and x (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])).", + "a x0", + "=> (and (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (and x (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2141, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]); [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c p8", + "=> (p8 p@type@2 and_i@type x1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 440, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]].", + "intro.", + "intro.", + 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"a not_e", + "=> (not (not [[false -> ('P : prop) -> 'P] -> false])); (not [[false -> ('P : prop) -> 'P] -> false]).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [[false -> ('P : prop) -> 'P] -> false]))]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (not (not [[false -> ('P : prop) -> 'P] -> false]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [[false -> ('P : prop) -> 'P] -> false]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (not [[false -> ('P : prop) -> 'P] -> false]))]].", + "a x1", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal17).", + "a x", + "=> (not x0); x0.", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1467, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]))) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2155, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "c x2", + "=> (x2 or_il@type p6@type or_il p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2416, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a 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"c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11 p@type p).", + "a or_e", + "=> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 460, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + 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prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]].", + "c em", + "=> (em goal).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": 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-> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p7@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not false); false.", + "a 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exfalso", + "=> false.", + "a x0", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + 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-> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "c x1", + "=> (x1 or_il@type).", + "c x1", + "=> (x1 p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x1", + "=> (x1 goal4).", + "c x1", + "=> (x1 goal8).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 or_e@type).", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal14).", + "c x1", + "=> (x1 p8@type).", + "c em", + "=> (em p9@type).", + "c x3", + "=> (x3 x2).", + "c p11", + "=> (p11 not_i).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])); (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> false].", + "a x0", + "=> (and [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false] [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : 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'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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-> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "c x", + "=> (x and_el@type em@type and_el).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a exfalso", + "=> false.", + "c x", + "=> (x not_i@type goal1 not_i).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "c x", + "=> (x iff_el@type goal10 iff_el).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]] -> false]].", + "c x", + "=> (x p5@type or_ir@type p5).", + "c em", + "=> (em goal16).", + "c x", + "=> (x p4@type goal16 p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 456, + "actions": 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a x0", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8622, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c x0", + "=> (x0 goal8 iff_er@type).", + "c em", + "=> (em p0@type).", + "c x0", + "=> (x0 p8@type@2 p7@type@1).", + "c iff_el", + "=> (iff_el p9@type@1 p8@type@2 p9).", + "c x0", + "=> (x0 goal2 p7@type).", + "c x0", + "=> (x0 p7@type@1@2 not_i@type).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p7@type@1 goal8 p7).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p11@type@1 goal2 p11).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c iff_er", + "=> (iff_er p12@type@1 p7@type@1@2 p12)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 340, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e not_e@type x1 not_e).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c x1", + "=> (x1 exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal6).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em not_i@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> 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-> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])); (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))).", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1823, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [false -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x", + "=> (x p1@type p1@type p1).", + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 659, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(and (or x x2) (or x (not x2))) -> x]; [x -> (and (or x x2) (or x (not x2)))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em x).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or x (not x))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em exfalso@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not (or [('P : prop) 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'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c and_er", + "=> (and_er p0@type not_e@type p3).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x", + "=> (x not_e@type iff_el@type not_e iff_el).", + "c x", + "=> (x iff_el@type iff_er@type iff_el iff_er).", + "c and_er", + "=> (and_er not_e@type iff_el@type p6).", + "c x", + "=> (x em@type exfalso@type em exfalso).", + "c and_el", + "=> (and_el not_e@type iff_el@type p6).", + "c and_el", + "=> (and_el em@type exfalso@type p9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false].", + "c em", + "=> (em goal3)." + ] + } + ], + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19318, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 835, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]; [(not (or false (not false))) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]].", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 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[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] -> [false -> [[(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] -> [[(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] -> [(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]]]]]) -> [[[(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] -> [(or false (not false)) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]] -> false]].", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal2).", + "c em", + "=> (em goal3).", + "c em", + "=> (em em@type).", + "c em", + "=> (em p7@type).", + "c em", + "=> (em p9@type).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em p8@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p1@type)." + ] + }, + { + "mode": 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> (not [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))])] (not [false -> (not [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))])]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a and_i", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and false (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))).", + "a x", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and false (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))).", + "a x", + "=> (and (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 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-> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and false (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and false (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))))))]; [(not (not [('P : prop) -> 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))))))].", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and false (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not 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'R] false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 620, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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: prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 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false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [false -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]; [(not [(not [false -> ('P : prop) -> 'P]) -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [(not [false -> ('P : prop) -> 'P]) -> false])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]]; [(not [(not [false -> ('P : prop) -> 'P]) -> false]) -> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))])); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + 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x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 492, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) 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'P))]))].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not x0) (not (not x0)))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not x0) (not (not x0))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or (not x0) (not (not x0))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not x0) 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prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> false].", + "c x", + "=> (x iff_i@type goal10 iff_i).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x", + "=> (x p0@type or_ir@type p0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x not_e@type iff_er@type not_e).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 507, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [x -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 721, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + 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false]].", + "c em", + "=> (em goal0@2).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(iff x (not x0)) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (iff x (not x0))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em goal0@1).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(iff x x0) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not (iff x x0)) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em goal0@2@2).", + "c iff_er", + "=> (iff_er x x0 x2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a x4", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c iff_el", + "=> (iff_el x x0 x2).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 517, + 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-> (or [('P : prop) -> (not 'P) -> 'P -> false] false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] false)].", + "intro.", + "a or_il", + "=> .", + "c em", + "=> (em goal3).", + "c em", + "=> (em p4@type@2).", + "intro.", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]." + ] + } + ], + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 19304, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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(not 'A) 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> false].", + "c x", + "=> (x p@type em@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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(not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])] (not false)); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 514, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (iff x 'B) (and (or x (not 'B)) (or (not x) 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal3).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2382, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : 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-> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 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[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q 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-> ['P -> 'Q]])])))]]].", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 x3).", + "a x3", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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'C])] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", 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false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1459, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]] (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]] (and (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> 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('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em p4@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 343, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + 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: prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : 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em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2275, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type not_e@type p0 not_e).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type not_e@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c and_er", + "=> (and_er p0@type not_e@type p3).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x", + "=> (x not_e@type iff_el@type not_e iff_el).", + "c x", + "=> (x iff_el@type em@type iff_el em).", + "c and_er", + "=> (and_er not_e@type iff_el@type p6).", + "c x", + "=> (x em@type exfalso@type em exfalso).", + "c and_el", + "=> (and_el not_e@type iff_el@type p6).", + "c and_el", + "=> (and_el em@type exfalso@type p9).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c p11", + "=> (p11 not_i@type).", + "intro.", + "c and_er", + "=> (and_er em@type exfalso@type p9).", + "intro.", + "a p5", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c p10" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 784, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p1@type@2).", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p1@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p4@type).", + "c em", + "=> (em goal2).", + "c x", + "=> (x p3@type@2).", + "c x", + "=> (x p6@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p10@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p11@type@2).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p9@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1413, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x", + "=> (x p1@type p5@type p5)." + ] + } + ], + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 24751, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 192, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]; [(not false) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : 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-> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])); (not [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]).", + "a or_e", + "=> [false -> (not (not [false -> (not [('P : 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-> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P])]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P])].", + "a x", + "=> (and [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [false -> ('P : prop) -> 'P])] (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; (and false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + 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-> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em p2@type@2).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false]].", + "a x", + "=> (iff [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a iff_i", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false] -> [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false]].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 456, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7706, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B 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false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2011, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] 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'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]) -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])] (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]))]; [(or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em 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false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c not_e", + "=> (not_e and_el@type x1 and_el).", + "intro.", + "c em", + "=> (em goal10).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 515, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em 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'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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-> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em goal3).", + "intro.", + "c em", + "=> (em p0@type).", + "a x1", + "=> (or [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal12).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])); (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ['P -> false] -> (not 'P)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x3", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "dead", + "depth_used": 37, + "evals_used": 289, + "actions": [ + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('C : prop) -> (iff (and (or x x0) (or (not x) 'C)) (or (and x 'C) (and (not x) x0)))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('C : prop) -> (iff (and (or x x0) (or (not x) 'C)) (or (and x 'C) (and (not x) x0)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('C : prop) -> (iff (and (or x x0) (or (not x) 'C)) (or (and x 'C) (and (not x) x0)))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('C : prop) -> (iff (and (or x x0) (or (not x) 'C)) (or (and x 'C) (and (not x) x0)))]].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> 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-> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> 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-> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])))]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_ir@type p2 or_ir).", + "c x1", + "=> (x1 goal19 not_e@type x).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1851, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_ir", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4272, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not false)].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2454, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11 em@type em).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not 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('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x not_i@type p3 not_i).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1596, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> false] (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]]) -> false].", + "c x", + "=> (x p@type p3@type@2 p).", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3486, + "actions": [ + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : 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-> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))]).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em goal).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))]) -> false].", + "a x0", + "=> (iff false (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))])).", + "a exfalso", + "=> .", + "a not_i", + 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prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q 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: prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))]].", + "a exfalso", + "=> 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'Q)]) -> false]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [[false -> ('P : prop) -> 'P] -> false])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] (not [false -> ('P : prop) -> 'P])); [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] (not [false -> ('P : prop) -> 'P]))]; [[(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> (or [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] (not [false -> ('P : prop) -> 'P]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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"=> (em p11@type@2).", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5038, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> (not 'P) -> 'P -> 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x0", + "=> (x0 em@type goal3 iff_i@type).", + "c x0", + "=> (x0 not_e@type iff_el@type not_e@type).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 and_er@type iff_el@type goal2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c not_e", + "=> (not_e or_e@type x2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a not_e", + "=> (not x); x.", + "c x0", + "=> (x0 goal3 iff_er@type exfalso@type)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..df90b9e50653b6ea2ad9709e0db6aff615bb4239 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,824 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[ ] - extrinsic_L0_7 (traces=17 evals=15242) +[ ] - extrinsic_L0_5 (traces=17 evals=23401) +[ ] - extrinsic_L0_3 (traces=17 evals=21490) + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L0_10 (traces=5 evals=1806) + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_1 (traces=11 evals=19128) +[ ] - extrinsic_L0_6 (traces=14 evals=36941) +[ ] - extrinsic_L0_4 (traces=17 evals=38197) +[ ] - extrinsic_L0_8 (traces=6 evals=20205) +[ ] - extrinsic_L0_9 (traces=13 evals=29638) +[ ] - extrinsic_L0_12 (traces=17 evals=23734) +[ ] - extrinsic_L0_11 (traces=14 evals=28586) +[ ] - extrinsic_L0_13 (traces=17 evals=25950) +[ ] - extrinsic_L0_14 (traces=10 evals=18733) +[ ] - extrinsic_L1_3 (traces=17 evals=19703) +[ ] - extrinsic_L1_1 (traces=14 evals=20713) +[ ] - extrinsic_L1_2 (traces=14 evals=34009) + +thread '' (1252707) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_2 (traces=17 evals=21646) + +thread '' (1252707) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_4 (traces=14 evals=27115) +[ ] - extrinsic_L2_1 (traces=13 evals=22614) +[ ] - extrinsic_L2_3 (traces=17 evals=14672) +[ ] - extrinsic_L2_6 (traces=17 evals=15388) + +thread '' (1252707) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_7 (traces=17 evals=22798) +[ ] - extrinsic_L2_4 (traces=15 evals=18371) +[ ] - extrinsic_L2_5 (traces=17 evals=31509) +[ ] - extrinsic_L2_8 (traces=11 evals=17042) +[ ] - extrinsic_L2_9 (traces=17 evals=21323) + +thread '' (1252706) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_12 (traces=17 evals=21875) + +thread '' (1252706) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_10 (traces=14 evals=24878) +[ ] - extrinsic_L2_11 (traces=17 evals=23331) +[ ] - extrinsic_L2_13 (traces=13 evals=16470) +[ ] - extrinsic_L3_1 (traces=11 evals=25673) + +thread '' (1252706) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1252706) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1252701) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1252701) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=17 evals=32752) +[ ] - extrinsic_L3_2 (traces=14 evals=18738) +[ ] - extrinsic_L3_4 (traces=15 evals=26856) +[ ] - extrinsic_L3_5 (traces=17 evals=28055) +[ ] - extrinsic_L3_6 (traces=17 evals=23987) +[ ] - extrinsic_L3_7 (traces=15 evals=27286) +[ ] - extrinsic_L3_8 (traces=17 evals=13440) +[ ] - extrinsic_L3_10 (traces=17 evals=16997) +[ ] - extrinsic_L3_11 (traces=17 evals=17998) +[ ] - extrinsic_L3_9 (traces=15 evals=29839) +[ ] - extrinsic_L3_12 (traces=17 evals=15946) + +thread '' (1252707) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1252707) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_14 (traces=17 evals=25929) +[ ] - extrinsic_L3_18 (traces=17 evals=16600) +[ ] - extrinsic_L3_13 (traces=17 evals=14651) +[ ] - extrinsic_L3_15 (traces=10 evals=20930) +[ ] - extrinsic_L3_16 (traces=17 evals=29490) +[ ] - extrinsic_L3_17 (traces=4 evals=17107) +[ ] - extrinsic_L3_21 (traces=17 evals=27418) +[ ] - extrinsic_L3_19 (traces=17 evals=25732) +[ ] - extrinsic_L3_20 (traces=10 evals=11144) +[ ] - extrinsic_L3_23 (traces=17 evals=21025) +[ ] - extrinsic_L3_22 (traces=17 evals=20183) +[ ] - extrinsic_L3_24 (traces=13 evals=26238) +[ ] - extrinsic_L3_26 (traces=17 evals=17218) +[ ] - extrinsic_L3_25 (traces=8 evals=12125) +[ ] - extrinsic_L3_27 (traces=17 evals=23643) +[ ] - extrinsic_L3_28 (traces=15 evals=21537) +[ ] - extrinsic_L3_29 (traces=12 evals=30345) +[ ] - extrinsic_L4_1 (traces=17 evals=18927) +[ ] - extrinsic_L4_2 (traces=14 evals=27550) + +thread '' (1252704) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1252704) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=15 evals=24636) +[ ] - extrinsic_L4_4 (traces=17 evals=24198) +[ ] - extrinsic_L4_5 (traces=17 evals=27407) +[ ] - extrinsic_L4_6 (traces=11 evals=21214) +[ ] - extrinsic_L4_9 (traces=17 evals=10475) +[ ] - extrinsic_L4_7 (traces=14 evals=19566) + +thread '' (1252705) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1252705) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_10 (traces=17 evals=13851) +[ ] - extrinsic_L4_8 (traces=13 evals=39624) +[ ] - extrinsic_L4_13 (traces=17 evals=27555) +[ ] - extrinsic_L4_12 (traces=13 evals=19656) +[ ] - extrinsic_L5_1 (traces=17 evals=24854) +[ ] - extrinsic_L4_11 (traces=15 evals=22606) +[ ] - extrinsic_L5_2 (traces=17 evals=30735) +[ ] - extrinsic_L4_14 (traces=15 evals=26629) +[ ] - extrinsic_L5_5 (traces=17 evals=19318) +[ ] - extrinsic_L5_4 (traces=17 evals=25422) +[ ] - extrinsic_L5_8 (traces=17 evals=33431) +[ ] - extrinsic_L5_6 (traces=17 evals=28813) +[ ] - extrinsic_L5_7 (traces=13 evals=19304) +[ ] - extrinsic_L5_3 (traces=7 evals=17693) + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_11 (traces=17 evals=13462) +[ ] - extrinsic_L5_9 (traces=14 evals=23478) +[ ] - extrinsic_L6_1 (traces=17 evals=14425) +[ ] - extrinsic_L5_10 (traces=15 evals=20033) + +thread '' (1252708) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_2 (traces=14 evals=24751) +[ ] - extrinsic_L6_3 (traces=17 evals=14296) +[ ] - extrinsic_L6_6 (traces=17 evals=37861) +[ ] - extrinsic_L6_4 (traces=15 evals=28283) +[ ] - extrinsic_L6_5 (traces=14 evals=25541) +[ ] - extrinsic_L6_7 (traces=15 evals=22251) +[ ] - extrinsic_L6_8 (traces=17 evals=22455) +[ ] - extrinsic_L6_9 (traces=4 evals=90438) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 2/94 in 8637.4s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..e52237ef367f8070333d5df0f6b97ceb234b3e2a --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,269 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L0_1 (traces=4 evals=13071) + +thread '' (1620922) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]) (x1 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] iff_el iff_el)): parameter type (and [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]])) and value type (and [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) did not unify. +[ ] - extrinsic_L0_2 (traces=17 evals=19849) +[ ] - extrinsic_L0_4 (traces=17 evals=25449) + +thread '' (1620927) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_3 (traces=12 evals=28881) +[ ] - extrinsic_L0_6 (traces=13 evals=37369) +[ ] - extrinsic_L0_5 (traces=14 evals=37855) +[OK ] - extrinsic_L0_10 (traces=5 evals=2981) +[ ] - extrinsic_L0_7 (traces=17 evals=14630) +[ ] - extrinsic_L0_8 (traces=16 evals=28313) +[ ] - extrinsic_L0_9 (traces=14 evals=35274) +[ ] - extrinsic_L0_13 (traces=17 evals=20231) + +thread '' (1620927) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x1 [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] iff_i or_il)): parameter type (and [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) did not unify. + +thread '' (1620927) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x1 [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] iff_i or_il)): parameter type (and [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) did not unify. +[ ] - extrinsic_L0_12 (traces=15 evals=19061) +[ ] - extrinsic_L0_11 (traces=14 evals=24552) +[ ] - extrinsic_L0_14 (traces=17 evals=15385) + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=17 evals=31695) + +thread '' (1620927) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620927) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_1 (traces=14 evals=20113) + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_2 (traces=11 evals=23907) + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_4 (traces=17 evals=38788) +[ ] - extrinsic_L2_1 (traces=14 evals=20086) +[ ] - extrinsic_L2_2 (traces=11 evals=24922) + +thread '' (1620928) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620928) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_3 (traces=15 evals=28561) +[ ] - extrinsic_L2_6 (traces=17 evals=24436) +[ ] - extrinsic_L2_4 (traces=15 evals=19592) + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620926) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620926) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620926) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_5 (traces=15 evals=17298) + +thread '' (1620929) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_7 (traces=16 evals=21868) +[ ] - extrinsic_L2_8 (traces=11 evals=28755) + +thread '' (1620925) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620925) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_9 (traces=14 evals=32059) +[ ] - extrinsic_L2_10 (traces=15 evals=20733) +[ ] - extrinsic_L2_11 (traces=11 evals=25268) +[ ] - extrinsic_L2_12 (traces=16 evals=27573) +[ ] - extrinsic_L2_13 (traces=13 evals=13939) +[ ] - extrinsic_L3_1 (traces=13 evals=16895) + +thread '' (1620928) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620928) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=17 evals=28115) +[ ] - extrinsic_L3_2 (traces=15 evals=29753) +[ ] - extrinsic_L3_4 (traces=17 evals=15242) +[ ] - extrinsic_L3_5 (traces=15 evals=11615) +[ ] - extrinsic_L3_6 (traces=13 evals=21198) + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=14 evals=27116) + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620922) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_8 (traces=17 evals=22336) +[ ] - extrinsic_L3_11 (traces=17 evals=25466) +[ ] - extrinsic_L3_10 (traces=17 evals=21211) +[ ] - extrinsic_L3_9 (traces=13 evals=20145) +[ ] - extrinsic_L3_12 (traces=13 evals=23995) diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..a0914671065cc73295792b2e4196ba14cff85ba7 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 18 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s42/train.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/train.log new file mode 100644 index 0000000000000000000000000000000000000000..59724ad89967fb6f2d20a50abc524e8b271c3ca4 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s42/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070920-zatscv5s +[2026-06-29T07:09:16.644667] Seeded RNGs with seed=42 +[2026-06-29T07:09:16.644877] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-29T07:09:19.984528] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json + 526 training examples loaded. + +============================================================ +[2026-06-29T07:09:19.985588] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 526 -> 526 unique examples + Epoch 1/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 18 total steps, 526 unique examples (batch_size=64) +[2026-06-29T07:09:23.909725] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:23.916349] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s42/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 18} diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/summary.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..1a211a35944e69ff817fe067f836ce65f6a4f797 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + 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false))] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and [false -> ('P : prop) -> 'P] (and false false))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [false -> ('P : prop) -> 'P] (and false false))]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and [false -> ('P : prop) -> 'P] (and false false))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [[[('P : prop) -> (not 'P) -> 'P -> false] -> (and [false -> ('P : prop) -> 'P] (and false false))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]).", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x).", + "c x1", + "=> (x1 exfalso@type goal8 p6).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ['A -> 'A]])).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ['A -> 'A]]))]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ['A -> 'A]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6220, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "a not_i", + "=> [[false -> false] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [false -> false] (or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])); [[false -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 301, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4812, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 or_e@type).", + "a x0", + "=> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]].", + "c p5", + "=> (p5 or_e).", + "c p5", + "=> (p5 p6).", + "a p7", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [x -> x])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]])]; [(not [x -> x]) -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> x]])].", + "a p7", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) (or [x -> x] (not [x -> x]))); [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [x -> x]))]; [(or [x -> x] (not [x -> x])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [x -> x]))].", + "a p6", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (not [('P : prop) -> (or 'P (not 'P))]) (or [x -> x] (not [x -> x])))]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (or (not [('P : prop) -> (or 'P (not 'P))]) (or [x -> x] (not [x -> x])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4870, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> false]].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]].", + "a exfalso", + 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-> (and 'P 'Q) -> 'P] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 432, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal3).", + "a x1", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]].", + "a x1", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal17).", + "a x", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])))).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false]; (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))).", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> (and [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> (and [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false] [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1937, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c x0", + "=> (x0 not_i@type false not_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1463, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type p0@type@2 not_e).", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[false -> ('P : prop) -> 'P] -> (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not false)]; [(not false) -> (not 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 35, + "evals_used": 2037, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c and_el", + "=> (and_el not_e@type p2@type p3).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c x1", + "=> (x1 iff_i@type or_e@type iff_i or_e).", + "c and_el", + "=> (and_el p0@type exfalso@type p5).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "c em" + ] + } + ], + "problem": "extrinsic_L0_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 31892, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 163, + "actions": [ + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]]; 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-> 'P]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "c x0", + "=> (x0 and_el@type goal1 and_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "c x0", + "=> (x0 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 or_e@type goal15 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p2@type not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (not false) [('P : prop) -> (not 'P) -> 'P -> false]); [(not false) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or (not false) [('P : prop) -> (not 'P) -> 'P -> false])]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> (or (not false) [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not false)]; [(not false) -> (not false)].", + "a or_e", + "=> [false -> [false -> (not false)]]; [(not false) -> [false -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [false -> [false -> (not false)]] (not [false -> [false -> (not false)]])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x0).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [false -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not false) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2370, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]); [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p@type p).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type not_i@type not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))))]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4582, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type or_ir@type x).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em 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-> (or 'P 'Q)]))].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal12)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2239, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P 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+ "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2288, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false 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: prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9745, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> 'B -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 or_ir).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type or_ir@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 em@type p6@type em p6).", + "c x1", + "=> (x1 p3@type p1@type p3 p1).", + "c x1", + "=> (x1 p14@type and_i@type p14 x0).", + "c x0", + "=> (x0 and_er@type not_e@type and_er not_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2565, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p2@type x1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R 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+ "=> (and_er goal p6@type p11).", + "c p12", + "=> (p12 or_ir@type p7@type p0 p7).", + "a exfalso", + "=> false.", + "c p12", + "=> (p12 and_i@type iff_i@type and_i iff_i).", + "c x", + "=> (x p5@type not_e@type p5 not_e).", + "c and_el", + "=> (and_el goal p8@type p11).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el goal p11@type p11).", + "c and_el", + "=> (and_el goal iff_i@type p11).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x0 -> x]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x0 -> x]].", + "c iff_el", + "=> (iff_el x x0 x1).", + "a 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]].", + "a x2", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]]).", + "c em", + "=> (em goal17).", + "a x2", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]])).", + "a x2", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]]))).", + "a and_i", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 398, + "actions": [ + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal9).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 582, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 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(or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]]].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": 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-> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (or [('P : prop) -> 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-> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1473, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x goal not_i@type not_e).", + "c x", + "=> (x iff_i@type and_el@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('A : prop) -> (not 'A) -> 'A -> false])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('A : prop) -> (not 'A) -> 'A -> false]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('A : prop) -> (not 'A) -> 'A -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('A : prop) -> (not 'A) -> 'A -> false]))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "a x", + "=> (or (or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[false -> ('P : prop) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not false) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 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x", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]).", + "a not_i", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": true, + "outcome": "solved", + "depth_used": 5, + "evals_used": 27, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> ." + ] + } + ], 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'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]) -> 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p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em or_e@type).", + "intro.", + "c em", + "=> (em goal16).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c x", + "=> (x p4@type@2).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1473, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", 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'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal15 em).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 460, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 em@type).", + "c x0", + "=> (x0 goal9).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type).", + "c x0", + "=> (x0 p4@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [false -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4589, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_ir", + "=> (not x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso em).", + "c em", + "=> (em goal4).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [x -> [x -> false]]; [(not x) -> [x -> false]].", + "a or_e", + "=> [x -> [x -> [x -> false]]]; [(not x) -> [x -> [x -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 6236, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> 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false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a x", + "=> (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a x", + "=> (or (or (not (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> ('Q : prop) 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "a x", + "=> (iff [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a iff_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false] -> [('P : prop) -> (not 'P) -> 'P -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "a x", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) 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false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x1", + "=> (x1 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2035, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + 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: prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal p1@type not_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[x -> false] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x0).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c x2", + "=> (x2 exfalso@type em@type exfalso em).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em goal7).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p3@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_er@type x0 and_er).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or false (not false)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or false (not false)))); (not (or false (not false))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 550, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal2).", + "c em", + "=> (em and_el@type).", + "intro.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a x", + "=> false." + ] + } + ], + "problem": "extrinsic_L0_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 6, + "evals_used": 11415, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 293, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 436, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (or false (not false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or false (not false)))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or false (not false)))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or false (not false)))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or false (not false)))); (not (or false (not false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (or false (not false))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not (or false (not false))))].", + "intro.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or false (not false)))] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or false (not false)))])) -> (not (not (or false (not 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p0", + "=> (p0 false exfalso@type exfalso).", + "c x", + "=> (x p4@type iff_i@type p4 iff_i).", + "a or_e", + "=> [(or (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not (or (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]]].", + "c x", + "=> (x em@type and_i@type em x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : 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prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]]; [(not [false -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]].", + "c em", + "=> (em p9@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]])." + ] + }, + { + "mode": "sample", + 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]); [(or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [false -> (not (not false))]; [(not false) -> (not (not false))].", + "a x1", + "=> (iff false (not (not false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff false (not (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff false (not (not false)))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 644, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [x -> [(not x) -> x2]]); [x -> [(not x) -> x2]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em 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: prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (or [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]] (or (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> 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-> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]) false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]])) (and (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]])]) false)])]]))." + ] + }, + { + "mode": "sample", + 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'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 584, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "c x1", + "=> (x1 p@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x0", + "=> false.", + "a not_e", + "=> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c not_e", + "=> (not_e or_e@type x2 or_e).", + "c x1", + "=> (x1 or_ir@type).", + "a x0", + "=> .", + "intro.", + "c not_e", + "=> (not_e or_e@type x3 or_e).", + "c x1", + "=> (x1 iff_el@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3917, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", 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prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_ir@type p2 or_ir).", + "c x1", + "=> (x1 goal19 not_e@type x).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 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false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> false].", + "c x", + "=> (x p@type@2 or_il@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false); [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [false -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 633, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; 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false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))).", + "c x0", + "=> (x0 goal12 or_ir@type x0).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type p2@type x1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))) -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3194, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : 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-> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]].", + "intro.", + "c x0", + "=> (x0 p0@type and_i@type p0 and_i).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2110, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a 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'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[false -> ('P : prop) -> 'P] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type em@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type em@type not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or (or (not false) (not (not false))) [('P : prop) -> (or 'P (not 'P))]); [(or (not false) (not (not false))) -> 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: prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : 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'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]; [[('P : prop) -> ('Q : prop) -> 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-> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and [('P : prop) -> ['P -> false] -> (not 'P)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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-> 'R])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 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-> 'P -> (or 'P 'Q)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x iff_el@type x3 x2).", + "c em", + "=> (em p4@type).", + "c x", + "=> (x iff_el@type x3 iff_el).", + "a x2", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not false)]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": 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exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (not [false -> ('P : prop) -> 'P]))); [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P])]; [(not (not [false -> ('P : prop) -> 'P])) -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [false -> ('P : prop) -> 'P])].", + "a or_ir", + "=> (not (not [false -> ('P : prop) -> 'P])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c em", + "=> 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal0).", + "a x", + "=> false.", + "c em", + "=> (em goal11).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a x", + "=> false.", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> 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goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + 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'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 4234, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : 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[(or [('A : prop) -> (iff (and 'A 'A) 'A)] (not [('A : prop) -> (iff (and 'A 'A) 'A)])) -> false]; [(not (or [('A : prop) -> (iff (and 'A 'A) 'A)] (not [('A : prop) -> (iff (and 'A 'A) 'A)]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> (iff (and 'A 'A) 'A)] (not [('A : prop) -> (iff (and 'A 'A) 'A)])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [(or [('A : prop) -> (iff (and 'A 'A) 'A)] (not [('A : prop) -> (iff (and 'A 'A) 'A)])) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A 'A) 'A)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> (iff (and 'A 'A) 'A)]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + 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-> false] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]))); [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "a x1", + "=> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not (not false)) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2485, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 p0@type and_i@type p0 and_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el p0@type and_i@type p2).", + "c x0", + "=> (x0 iff_el@type p2@type iff_el p2).", + "c and_el", + "=> (and_el iff_el@type p2@type p4).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff (and x x) x)); (iff (and x x) x).", + "c and_er", + "=> (and_er iff_el@type p2@type p4).", + "a not_i", + "=> [(iff (and x x) x) -> false].", + "c and_el", + "=> (and_el p0@type and_i@type p6).", + "c and_er", + "=> (and_er p0@type and_i@type p6).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p2@type p2@type p2 p2).", + "c p8", + "=> (p8 p1@type p@type p1 p).", + "c and_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + 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false].", + "c em", + "=> (em goal12).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [x -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [x -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x3", + "=> (x3 iff_el@type or_ir@type iff_el or_ir).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 455, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> 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(not 'P) -> 'P -> false] -> false]]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]]].", + "intro.", + "c x1", + "=> (x1 not_e).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "c em", + "=> (em 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'P -> false]) -> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]]].", + "c x2", + "=> (x2 x).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> 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: prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal12)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 680, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [('A : prop) -> (iff (or 'A 'A) 'A)]].", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 and_el@type p1@type and_el).", + "c x0", + "=> (x0 and_el@type goal10 and_el)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1596, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> 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-> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "c x1", + "=> (x1 x false x0).", + "a exfalso", + "=> .", + "c em", + "=> (em p5@type@2).", + "c x1", + "=> (x1 x false x0).", + "intro.", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c x2", + "=> (x2 goal5).", + "c iff_el", + "=> (iff_el p8@type@1 false p8).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "c iff_er", + "=> (iff_er p8@type@1 false p8).", + "intro.", + "c x2", + "=> (x2 not_e@type).", + "c p12", + "=> (p12 p3).", + "c x4" + ] + }, + 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-> [(and x false) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(and x false) -> false]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not 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(iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal0).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(and x false) -> false]]] -> (not 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"=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 false p5).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c x", + "=> (x p@type@2).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff (and 'A false) false)]); [('A : prop) -> (iff (and 'A false) false)].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> (iff (and 'A false) false)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> (iff (and 'A false) false)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> (iff (and 'A false) false)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A false) false)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A false) false)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + 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'Q)]) (not [false -> ('P : prop) -> 'P]))].", + "a x0", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [false -> ('P : prop) -> 'P]) -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "c em", + "=> (em not_i@type).", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P]))); [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[false -> ('P : prop) -> 'P] -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em x2).", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_ir", + "=> .", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x1", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 869, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p3@type iff_el p3).", + "a exfalso", + "=> false.", + "a x1", + "=> (and x false).", + "c x1", + "=> (x1 iff_el@type p3@type p5).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_el@type p3@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6339, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))].", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 p6@type p1@type p6).", + "c em", + "=> (em p0@type@2).", + "c x0", + "=> (x0 p8@type x p8).", + "c iff_el", + "=> (iff_el x p9@type@2 p9).", + "c x0", + "=> (x0 em@type iff_er@type em).", + "c x0", + "=> (x0 p3@type p9@type@2 p3).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p1@type p7@type@2 p7).", + "c iff_el", + "=> (iff_el iff_er@type p11@type@2 p11).", + "c iff_er", + "=> (iff_er x p9@type@2 p9).", + "c iff_el", + "=> (iff_el p9@type@2 p12@type@2 p12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 p11@type p0@type@2 p11)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]])].", + "a x", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> (not [false -> ('P : prop) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] false).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; false.", + "intro.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a x", + "=> (and [(not [false -> ('P : prop) -> 'P]) -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(not [false -> ('P : prop) -> 'P]) -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(not [false -> ('P : prop) -> 'P]) -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] false))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) 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false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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"c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p12@type and_er p12)." + ] + } + ], + "problem": "extrinsic_L2_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 11035, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q 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false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [x0 -> x0]]).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)])); [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 625, + "actions": [ + "c 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['P -> false] -> (not 'P)])) -> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (and (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3875, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_il", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a x1", + "=> (or (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]))]]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x not_i@type x3 not_i).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 not_i@type x3 not_i).", + "c x2", + "=> (x2 not_i@type x3 not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 408, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1351, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1947, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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-> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : 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[('P : prop) -> (not 'P) -> 'P -> false] (and [('P : prop) -> (or 'P (not 'P))] false)) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) (and false (and false (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (and [('P : prop) -> (not 'P) -> 'P -> false] (and [('P : prop) -> (or 'P (not 'P))] false)) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) (and false (and false (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and (and (and [('P : prop) -> (not 'P) -> 'P -> false] (and [('P : prop) -> (or 'P (not 'P))] false)) (and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) (and false (and false (and [('P : prop) -> ('Q : prop) 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'C]] -> ['B -> ['A -> 'C]]] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x1", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "c em", + "=> (em goal20).", + "c x3", + "=> (x3 x1).", + "a x1", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1390, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))); (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 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"intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) (not false)); [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or false (not false)) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 47, + "evals_used": 4431, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", 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false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> 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+ "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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'R] -> 'R])))]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])))]]).", + "c em", + "=> (em goal18).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] false).", + "a and_i", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "c em", + "=> (em em@type).", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> (or 'P (not 'P))]) false).", + "a x0", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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[false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]])) (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2914, + "actions": [ + "c em", + "=> (em or_il@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 and_el@type or_ir@type and_el).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p4@type iff_el).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_e@type iff_i@type or_e).", + "c x0", + "=> (x0 iff_i@type and_el@type iff_i).", + "c em", + "=> (em goal13).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em goal19)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1263, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em em@type).", + "a not_i", + "=> [x -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "c x1", + "=> (x1 p1@type p4@type p1 p4).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c em", + "=> (em p3@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[false -> ('P : prop) -> 'P] -> false] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[false -> ('P : prop) -> 'P] -> false] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]))]." + ] + }, + { + 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false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + 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[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 p@type@2 and_er@type and_er).", + "c x0", + "=> (x0 p@type@2 or_ir@type or_ir).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 exfalso@type iff_i@type iff_i)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]); 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exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 p@type@2 and_er@type and_er).", + "c x0", + "=> (x0 p@type@2 or_ir@type or_ir).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 exfalso@type exfalso@type exfalso)." + ] + }, + { + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + 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exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", 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-> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p4@type@2 or_e@type or_e).", + "a not_i", + "=> [false -> false].", + "intro.", + "c x0", + "=> (x0 p1@type p1@type p1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q 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[(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))] -> [false -> [false -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 8670, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P 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-> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]))).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 495, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type x2 and_i).", + "c em", + "=> (em p0@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))); (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "c x", + "=> (x and_i@type x2 and_i).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> (or 'P (not 'P))])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; (not [('P : prop) -> (or 'P (not 'P))]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false].", + "c x0", + "=> (x0 iff_i@type p@type p).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x", + "=> (x p@type p3@type@2 p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (and (not x) (not 'B)) -> (not (or x 'B))]].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em p1@type).", + "a x0", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2349, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])].", + "a exfalso", + "=> false.", 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['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 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-> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]]]].", + "a x2", + "=> (iff [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]]] [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal18).", + "c em", + "=> (em p4@type@2).", + "a iff_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]]] -> [('P : prop) -> (not 'P) -> 'P -> false]]; [[('P : prop) -> 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'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] 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-> x0]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1672, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em goal9).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]) -> false].", + "a x0", + "=> (iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> 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'P)]))))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p8@type).", + "c x", + "=> (x p2@type iff_er@type iff_er).", + "intro.", + "c x", + "=> (x p2@type em@type em)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1483, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) 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[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]]]]) -> false].", + "c x0", + "=> (x0 not_i@type p1@type p7 p1).", + "c and_el", + "=> (and_el not_i@type p1@type p9).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er not_i@type p1@type p9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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-> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 957, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal).", + "a 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1383, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [false -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false]]; [(not false) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + 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prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]]].", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x3", + "=> (x3 goal8 p@type p).", + "a not_i" 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(and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> 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exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a 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-> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 315, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 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('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) (and (and false [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]).", + "c em", + "=> (em goal9).", + "a and_i", + "=> false; [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "a or_e", + "=> [(and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + 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false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a x", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not (not [('P : prop) -> ('Q : 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(not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))))]].", + "a x", + "=> (and (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))))]]).", + "c em", + "=> (em goal18).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (and (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 465, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> 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-> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]] -> false]]].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + 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+ "c em", + "=> (em goal9).", + "c em", + "=> (em p5@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 538, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a 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[(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 471, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", 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-> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 403, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> [[false -> ('P : prop) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 446, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x0", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "c em", + "=> (em goal3).", + "intro.", + "c em", + "=> (em goal12).", + "a x0", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a and_i", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1460, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and false (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]; [(not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false]; [(not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4013, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)])]].", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)])]] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and (not x0) false).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (not x0) false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 433, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> (not (not (not 'A))) -> (not 'A)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [('A : prop) -> (not (not (not 'A))) -> (not 'A)].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2006, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_el@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (not (not x))) -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p0@type p4 p7).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x0", + "=> (x0 em@type or_ir@type em or_ir).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2415, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 or_e@type p@type p).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "c x0", + 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exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [false -> (not [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [(not false) -> (not [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] 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[('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p0@type@2).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal4).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false])); (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]).", + "a exfalso", + "=> false.", + "a x3", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p2@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 399, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + 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prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1405, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x1", + "=> (and false x).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal6).", + "a and_i", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5928, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])] -> false].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])] -> false]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]); [(or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a p4", + "=> (or (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]])))))))); [(or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) -> (or (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]; [(or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) -> (or (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))) (not (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])]]))))))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]])].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L3_19" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 8, + "evals_used": 7346, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + 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false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> 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-> 'R] -> 'R]) -> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 518, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 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prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and 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-> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not false) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]; [(not false) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not false) -> [('B : prop) -> ('C : prop) -> (or x (and 'B 'C)) -> (and (or x 'B) (or x 'C))]]]; [(not false) -> [(not false) 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false].", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_el@type and_el).", + "a or_e", + "=> [[(not [false -> ('P : prop) -> 'P]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "intro.", + "intro.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 477, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + 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'Q) -> ['Q -> 'P]] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]].", + "intro.", + "c em", + "=> (em goal8).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal3).", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> false].", + "a x0", + "=> false.", + "c em", + "=> (em goal13).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal18).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4632, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 and_er@type p1@type and_er).", + "c x1", + "=> (x1 p@type p@type p).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x1", + "=> (x1 p@type and_er@type p).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 or_il@type goal x1).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))); (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p3@type not_e@type x2).", + "c x1", + "=> (x1 p0@type goal0 p0).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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-> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 624, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [false -> 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 541, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])." + ] + } + ], + "problem": "extrinsic_L3_22" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 17105, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 448, + "actions": [ + "c em", + "=> (em false).", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]; [(not false) -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B].", 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-> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "c em", + "=> (em goal7).", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + 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-> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal).", + "c em", + "=> (em p4@type).", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]].", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])) -> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]]; [(not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 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[(or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])) -> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]]]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 495, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> 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false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x0", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not x); x.", + "c not_e", + "=> (not_e or_ir@type x2 or_ir).", + "c x1", + "=> (x1 p4 or_ir@type).", + "a x0", + "=> .", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> x]; [(not [false -> ('P : prop) -> 'P]) -> x].", + "a x0", + "=> false.", + "c not_e", + "=> (not_e or_ir@type x2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) 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prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x em@type p3 em).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 434, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x or_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6729, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])); [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [false -> (or (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (or 'P (not 'P))]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 501, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 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[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type).", + "c em", + "=> (em p3@type).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [false -> ('P : prop) -> 'P]); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [false -> ('P : prop) -> 'P])]; [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [false -> ('P : prop) -> 'P])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q 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false).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (and (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a x", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)].", + "intro.", + "a x", + "=> (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)))]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x0", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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+ "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]); [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]); [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))])]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 529, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> 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-> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 467, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em goal0).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em x).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal13).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 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false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q 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-> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> [(not (not 'A)) -> 'A]])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> [(not (not 'A)) -> 'A]]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 303, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 552, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + 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false]]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])))); (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + 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-> 'P])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5916, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + 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-> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "c x0", + "=> (x0 p@type and_er@type and_er).", + "c x0", + "=> (x0 p@type or_il@type or_il).", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [false -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 p@type@2 iff_i@type iff_i).", + "c x0", + "=> (x0 p@type@2 em@type em).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]])].", + "c x0", + "=> (x0 exfalso@type p0@type p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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"=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1339, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5790, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]].", + "c x0", + "=> (x0 not_e@type em@type not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) false); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [false -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8695, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "c x0", + "=> (x0 not_i@type or_e@type not_i or_e).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "c and_el", + "=> (and_el not_i@type or_e@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type 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-> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a x", + "=> (iff [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a iff_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a x", + "=> (iff (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 302, + "actions": [ + "c em", + "=> (em or_il@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a 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-> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))).", + "a x3", + "=> false.", + "a or_e", + "=> [(not x0) -> false]; [(not (not x0)) -> false].", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not (not x0)).", + "a or_e", + "=> [x0 -> (not (not x0))]; [(not x0) -> (not (not x0))].", + "intro.", + "c not_e", + "=> (not_e x0 x2 x4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 642, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] (and false (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] (and false (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x", + "=> (and [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [false -> ('P : prop) -> 'P] (and false (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)))]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]])); (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]).", + "a or_e", + "=> [false -> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]))]; [(not false) -> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]))].", + "a or_e", + "=> [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]))]]; [(not false) -> [false -> (not (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]))]].", + 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false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3917, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> ('Q : 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i iff_el).", + "c x2", + "=> (x2 p2@type or_il@type p2 x1).", + "c x1", + "=> (x1 p4@type em@type p4).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x p@type@2 or_ir@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P 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em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]].", + "c em", + "=> (em goal14).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]].", + "intro.", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (or 'P (not 'P))] -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not false) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [false -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not false) -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal2).", + "c em", + "=> (em p@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]); [false -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 564, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (not false)]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2156, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 15011, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a iff_i", + "=> [[x -> x2] -> (or (not x) x2)]; [(or (not x) x2) -> [x -> x2]].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p0@type@2 or_e@type or_e).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir x1).", + "c x1", + "=> (x1 not_i@type p5@type not_i p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false iff_el@type iff_el).", + "c x1", + "=> (x1 and_er@type p11@type and_er p11).", + "c p9", + "=> (p9 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4@1).", + "c p4", + "=> (p4 goal0 and_i@type p9).", + "c p4", + "=> (p4 p2@type and_i@type p9).", + "c p9", + "=> (p9 p8@type and_i@type p8 x1).", + "c p9", + "=> (p9 p17@type p17@type p17 p17).", + "c p4", + "=> (p4 or_ir@type p12@type p12).", + "c and_er", + "=> (and_er and_er@type p11@type p14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 53, + "evals_used": 3216, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "intro.", + "c x0", + "=> (x0 or_e@type p1@type p1).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x0", + "=> (x0 goal11 or_ir@type x0).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c x0", + "=> (x0 p2@type and_el@type and_el).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type and_el@type and_el)." + ] + } + ], + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 10, + "evals_used": 27232, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "c em", + "=> (em not_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11786, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> 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-> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_ir", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 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[false -> ('P : prop) -> 'P]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal7).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]); [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> .", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 891, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c x1", + "=> (x1 iff_el@type p3@type iff_el p3).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c and_el", + "=> (and_el iff_el@type p3@type p5).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4947, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c x0", + "=> (x0 p6@type p1@type@2 p6).", + "c x0", + "=> (x0 exfalso@type goal3 exfalso).", + "c x0", + "=> (x0 p8@type em@type p8).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 iff_el@type p6@type iff_el).", + "c x0", + "=> (x0 p3@type not_i@type p3).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p8@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 480, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em 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(not [false -> ('P : prop) -> 'P]))) -> (not (or false (not false)))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3214, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [false -> ('P : prop) 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])); (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x p@type@2 or_ir@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 38, + "evals_used": 1219, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_el@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em" + ] + } + ], + "problem": "extrinsic_L4_9" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19883, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 236, + "actions": [ + "intro.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_e@type).", + "intro.", + "c em", + "=> (em p0@type@2).", + "a or_ir", + "=> [x -> x0].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a and_i", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a x", + "=> (and (and [('P : prop) -> ('Q : 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false)))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))))))).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (not (not [('P 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(and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [false -> ('P : prop) -> 'P] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 614, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P 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'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] -> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] -> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] -> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))]]).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] -> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))]])).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] -> (not (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))]]).", + "c x3", + "=> (x3 iff_er@type exfalso@type iff_er exfalso).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 342, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em false).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [false -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 657, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x [x -> 'B])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x [x -> 'B])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : 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-> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))])].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)].", + "a x", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]]) -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]]).", + "c em", + "=> (em goal19).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] -> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 465, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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(em p3@type).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])))]; (and (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])))]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5203, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [x -> (not x)]) -> x]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [x -> (not x)]) -> x]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a 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-> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x and_i@type x3 and_i).", + "a exfalso", + "=> .", + "a x2", + "=> (iff [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))]] (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em goal9).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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exfalso", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [false -> ('P : prop) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])].", + "a x", + "=> (not [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])])]).", + "a not_i", + "=> [[[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])])])] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 518, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a 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+ "=> [[[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))] -> [[[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]) -> [[[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 x).", + "c x1", + "=> (x1 exfalso).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + 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false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 434, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]); [('A : prop) -> [(not 'A) -> 'A] -> 'A].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [x -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not x) -> [[('P 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal14 not_e).", + "a x", + "=> (or [('A : prop) -> [(not 'A) -> 'A] -> 'A] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]); [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('A : prop) -> [(not 'A) -> 'A] -> 'A] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('A : prop) -> [(not 'A) -> 'A] -> 'A] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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: prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10794, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_il", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> 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-> 'P -> 'Q -> (and 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : 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(iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x1", + "=> (x1 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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"=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1773, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 iff_i@type and_i@type and_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10525, + 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exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p5@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "intro.", + "c em", + "=> (em p7@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))); (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5249, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 369, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 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'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em or_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a x0", + "=> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_el@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) 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prop) -> 'P -> (or 'P 'Q)]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 882, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", 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(and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type or_ir@type iff_el or_ir).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "c x0", + "=> (x0 iff_el@type or_ir@type p4).", + "c em", + "=> (em goal14).", + "a and_i", + "=> false.", + "c and_er", + "=> (and_er iff_el@type or_ir@type p4).", + "c em", + "=> (em p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1823, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c not_e", + "=> (not_e iff_er@type x0 iff_er).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "c x0", + "=> (x0 p3@type@2 iff_el@type).", + "c em" + ] + }, + { + "mode": 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false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "c em", + "=> (em goal6).", + "c em", + "=> (em p2@type@2).", + "intro.", + "a not_e", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a not_i", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false].", + "a x0", + "=> false.", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal17).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 440, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", 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[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]))]].", + "a x1", + "=> false.", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a x1", + "=> false.", + "a x1", + "=> false.", + "c em", + "=> (em goal17).", + "a x", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x1", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> 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false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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: prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 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"=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; 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false] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]])].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]])]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not x); x.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not x2); x2.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or false (not false))).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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"=> (em goal).", + "c x0", + "=> (x0 goal9 or_e@type or_e).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "intro.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 660, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]] [('P : prop) -> ['P -> false] -> (not 'P)]) (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "intro.", + "a x0", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "a x", + "=> (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 505, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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-> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em p5@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 480, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + 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: prop) -> (and 'P 'Q) -> 'Q] -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P 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-> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6870, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + 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'P -> (or 'P 'Q)]))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]].", + "a x2", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P])].", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_el@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 52, + "evals_used": 2016, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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-> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a x0", + "=> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 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-> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))]].", + "intro.", + "a exfalso", + "=> false.", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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goal1).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]].", + "c x", + "=> (x p1@type@2).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]] -> false]].", + "c x", + "=> (x p7@type@2).", + "c em", + "=> (em p10@type@2).", + "c x", + "=> (x p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 452, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a 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false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5071, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + 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-> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p6@type@2 and_er@type and_er).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x1", + "=> (x1 em@type p8@type p8).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 465, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + 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(and 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 403, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2065, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : 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-> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not [x -> 'B]) (and x (not 'B)))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] -> 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]].", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 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'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]); [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> (not [('A : prop) -> ('B : prop) -> 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exfalso", + "=> false.", + "a x", + "=> (not [x0 -> false]); [x0 -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [x0 -> false])].", + "c and_el", + "=> (and_el and_er@type and_i@type p2).", + "intro.", + "c and_er", + "=> (and_er and_er@type and_i@type p2).", + "c p7", + "=> (p7 and_er@type p4@type and_er p4).", + "c x3", + "=> (x3 and_el@type em@type and_el em).", + "c x2", + "=> (x2 p0@type and_i@type p0 and_i).", + "c p7", + "=> (p7 iff_er@type p@type iff_er p).", + "c p7", + "=> (p7 p5@type and_i@type p5 p7).", + "c p6", + "=> (p6 p5@type and_i@type p12).", + "a p6", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [x0 -> false])).", + "a p6" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 397, + "actions": [ 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 428, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2449, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a x0", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a x1", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em goal10).", + "a x1", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] (not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 327, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + 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'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 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-> (not 'P)]) -> false].", + "c em", + "=> (em x0).", + "a or_e", + "=> [[x0 -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [x0 -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a or_e", + "=> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [x0 -> false]) -> [[x0 -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a or_e", + "=> [[x0 -> false] -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]]; [(not [x0 -> false]) -> [[x0 -> false] -> [[x0 -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]].", + "intro.", + "c x1", + "=> (x1 x0 x5).", + "a exfalso", + "=> false.", + "c x5", + "=> (x5 x2).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal0@1@1).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em or_il@type).", + "a or_e" + ] + 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-> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false].", + "c em", + "=> (em p0@type).", + "intro.", + "a x0", + "=> .", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false]].", + "a x", + "=> (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "a x", + "=> (iff (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (iff [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 698, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]])).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)].", + "intro.", + "a x1", + "=> (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)))]].", + "intro.", + "c em", + "=> (em iff_er@type).", + "a x1", + "=> (and (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false)))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 514, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [false -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]]; [(not false) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]) -> false].", + "a or_e", + "=> [(not false) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> false]]; [(not (not false)) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] -> [(not false) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> false]]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]) -> [(not false) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> false]]].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 553, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal7).", + "c em", + "=> (em and_el@type).", + "intro.", + "c x1", + "=> (x1 iff_el@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em and_er@type).", + "a x0", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal7).", + "a x0" + ] + } + ], + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 6, + "evals_used": 15182, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a 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and_i", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3445, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 iff_i@type p2@type@2 iff_i).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "c x0", + "=> (x0 p2@type p4@type p2).", + "c em", + "=> (em goal19).", + "c x0", + "=> (x0 p2@type goal8 p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 968, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "c em", + "=> (em not_i@type).", + "a x1", + "=> false.", + "c x1", + "=> (x1 exfalso@type iff_el@type exfalso iff_el).", + "a exfalso", + "=> false.", + "c and_el", + 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exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x0", + "=> (x0 goal8 iff_er@type).", + "c em", + "=> (em p0@type).", + "c x0", + "=> (x0 p8@type@2 p7@type@2@2@1).", + "c iff_el", + "=> (iff_el p9@type@1 p9@type@2 p9).", + "c x0", + "=> (x0 p2@type iff_el@type).", + "c x0", + "=> (x0 p7@type@2 p11@type@2@2).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p7@type@1 p7@type@2 p7).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p11@type@1 p11@type@2 p11).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c iff_er" + ] + } + ], + "problem": "extrinsic_L5_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 25808, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 615, + "actions": [ + "intro.", + "c em", + "=> (em x).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]].", + "a or_e", + "=> [x -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]]; [(not x) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]].", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em goal6).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) 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"c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1331, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 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false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : 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exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[(or [('P : prop) -> ('Q : 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-> false]]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [x -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]." + ] + }, + { + "mode": 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exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x p3@type@2 goal17 iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5454, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c em", + "=> (em goal7).", + "a x0", + "=> (or (not false) (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))); [(not false) -> false]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a x0", + "=> (or (not false) (not [false -> ('P : prop) -> 'P])); [(not false) -> (or (not false) (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [false -> ('P : prop) -> 'P]) -> (or (not false) (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 467, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]].", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]]].", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1453, + "actions": [ + "c em", + "=> (em or_il@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "c x0", + "=> (x0 iff_el@type p4@type iff_el).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c em", + "=> 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x0", + "=> (iff 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]))); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false]]; [(or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x3", + "=> .", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 727, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (iff (or (and x 'B) (and (not x) 'C)) (and (or x 'C) (or (not x) 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> (iff (or (and x 'B) (and (not x) 'C)) (and (or x 'C) (or (not x) 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c x0", + "=> (x0 goal8).", + "c x0", + "=> (x0 p@type@2).", + "c x0", + "=> (x0 p8@type@2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type).", + "c x0", + "=> (x0 p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 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false]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) 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+ "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not (not [false -> ('P : prop) -> 'P]))); (not (not [false -> ('P : prop) -> 'P])).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + 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'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 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-> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 519, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> (iff (or x (iff 'B 'C)) (iff (or x 'B) (or x 'C)))]]; [(not false) -> [('B : prop) -> ('C : prop) -> (iff (or x (iff 'B 'C)) (iff (or x 'B) (or x 'C)))]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> (iff (or x (iff 'B 'C)) (iff (or x 'B) (or x 'C)))]]; [(not false) -> [('B : prop) -> ('C : prop) -> (iff (or x (iff 'B 'C)) (iff (or x 'B) (or x 'C)))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + 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'Q)] (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]))).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] 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prop) -> ['P -> false] -> (not 'P)])]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]]).", + "c em", + "=> (em goal18).", + "a x0", + "=> (and (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + 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('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> 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'P -> false] -> false])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]); [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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: prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> ('D : prop) -> [x -> 'B] -> ['C -> 'D] -> [(and x 'C) -> (and 'B 'D)]]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 541, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P 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'R] -> ['Q -> 'R] -> 'R] -> (not (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 683, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : 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[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + 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or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (not (not [false -> ('P : prop) -> 'P]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; (not (not [false -> ('P : prop) -> 'P])).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [false -> ('P : prop) -> 'P])) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2293, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 and_i@type iff_i@type and_i).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x0", + "=> (x0 not_i@type em@type not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "c em", + "=> (em goal3).", + "intro.", + "c em", + "=> (em goal8).", + "c x0", + "=> (x0 iff_el@type p0@type@2 iff_el).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P 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-> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3486, + "actions": [ + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c x1", + "=> (x1 goal3).", + "c x1", + "=> (x1 goal7).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 or_ir@type).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]].", + "c and_el", + "=> (and_el and_el@type p@type p1).", + "intro.", + "intro.", + "c not_e", + "=> (not_e em@type x3 x1).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c and_er", + "=> (and_er and_el@type p@type p1).", + "c p8", + "=> (p8 and_el@type p@type p1).", + "c p11", + "=> (p11 and_el@type p@type p1).", + "c p12", + "=> (p12 and_el@type p@type p1).", + "a p12", + "=> (and [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]] (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false] (not [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]))).", + "c x2", + "=> (x2 or_e@type p0@type@2 or_e x4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 403, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [false -> ('P : prop) -> 'P]) -> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]])) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6418, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]); [[('P : prop) -> (or 'P (not 'P))] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type em@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..13fb1e684f751bdaf948eea07d15ac5d88a801bb --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,962 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[ ] - extrinsic_L0_5 (traces=17 evals=31892) +[ ] - extrinsic_L0_1 (traces=17 evals=26867) +[ ] - extrinsic_L0_3 (traces=16 evals=20596) +[ ] - extrinsic_L0_4 (traces=13 evals=32861) +[ ] - extrinsic_L0_6 (traces=15 evals=27344) +[ ] - extrinsic_L0_7 (traces=17 evals=24236) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L0_10 (traces=5 evals=1825) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (x [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] iff_er and_i)): parameter type (and [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) and value type (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) did not unify. + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_13 (traces=17 evals=15343) + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x1 [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] iff_i or_il)): parameter type (and [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253106) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x1 [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] iff_i or_il)): parameter type (and [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) did not unify. +[ ] - extrinsic_L0_9 (traces=13 evals=38773) +[ ] - extrinsic_L0_8 (traces=11 evals=18606) +[ ] - extrinsic_L0_11 (traces=13 evals=18405) +[ ] - extrinsic_L0_12 (traces=15 evals=23776) + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_14 (traces=6 evals=11415) + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_1 (traces=17 evals=21622) +[ ] - extrinsic_L1_1 (traces=17 evals=29969) +[ ] - extrinsic_L2_2 (traces=17 evals=17064) +[ ] - extrinsic_L1_4 (traces=17 evals=21328) +[ ] - extrinsic_L1_2 (traces=17 evals=28549) +[ ] - extrinsic_L1_3 (traces=15 evals=24936) + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_3 (traces=8 evals=15765) +[ ] - extrinsic_L2_5 (traces=17 evals=20263) +[ ] - extrinsic_L2_4 (traces=15 evals=18426) +[ ] - extrinsic_L2_6 (traces=13 evals=29064) +[ ] - extrinsic_L2_7 (traces=14 evals=30365) +[ ] - extrinsic_L2_8 (traces=17 evals=18891) +[ ] - extrinsic_L2_11 (traces=17 evals=11035) +[ ] - extrinsic_L2_9 (traces=17 evals=19399) +[ ] - extrinsic_L2_12 (traces=17 evals=21499) +[ ] - extrinsic_L2_10 (traces=13 evals=26745) +[ ] - extrinsic_L2_13 (traces=13 evals=20483) +[ ] - extrinsic_L3_1 (traces=13 evals=13950) + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=11 evals=12626) +[ ] - extrinsic_L3_3 (traces=14 evals=28524) +[ ] - extrinsic_L3_5 (traces=17 evals=26000) +[ ] - extrinsic_L3_4 (traces=15 evals=30101) + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=11 evals=12930) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=13 evals=31345) + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_8 (traces=17 evals=24701) +[ ] - extrinsic_L3_9 (traces=17 evals=20659) +[ ] - extrinsic_L3_11 (traces=17 evals=28323) +[ ] - extrinsic_L3_10 (traces=15 evals=15935) +[ ] - extrinsic_L3_12 (traces=17 evals=20298) +[ ] - extrinsic_L3_15 (traces=17 evals=12366) +[ ] - extrinsic_L3_14 (traces=17 evals=14766) +[ ] - extrinsic_L3_13 (traces=17 evals=29643) +[ ] - extrinsic_L3_18 (traces=17 evals=22647) +[ ] - extrinsic_L3_16 (traces=14 evals=16735) +[ ] - extrinsic_L3_17 (traces=17 evals=26238) +[ ] - extrinsic_L3_20 (traces=8 evals=7346) +[ ] - extrinsic_L3_21 (traces=17 evals=14690) +[ ] - extrinsic_L3_22 (traces=17 evals=16362) +[ ] - extrinsic_L3_23 (traces=17 evals=17105) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=8 evals=10545) + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=17 evals=20815) + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253105) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_25 (traces=17 evals=17163) +[ ] - extrinsic_L3_26 (traces=17 evals=28080) +[ ] - extrinsic_L3_27 (traces=15 evals=27400) +[ ] - extrinsic_L3_28 (traces=16 evals=26493) +[ ] - extrinsic_L3_29 (traces=14 evals=17843) +[ ] - extrinsic_L4_1 (traces=14 evals=29515) +[ ] - extrinsic_L4_2 (traces=17 evals=17010) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253104) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253104) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253108) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=15 evals=27391) +[ ] - extrinsic_L4_6 (traces=17 evals=20058) +[ ] - extrinsic_L4_4 (traces=15 evals=37251) +[ ] - extrinsic_L4_5 (traces=15 evals=34351) + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253101) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_7 (traces=17 evals=35640) +[ ] - extrinsic_L4_8 (traces=14 evals=26323) +[ ] - extrinsic_L4_10 (traces=17 evals=19883) +[ ] - extrinsic_L4_11 (traces=17 evals=20067) +[ ] - extrinsic_L4_9 (traces=10 evals=27232) +[ ] - extrinsic_L4_12 (traces=14 evals=20119) +[ ] - extrinsic_L4_13 (traces=15 evals=38576) +[ ] - extrinsic_L4_14 (traces=11 evals=15628) +[ ] - extrinsic_L5_3 (traces=17 evals=13094) +[ ] - extrinsic_L5_1 (traces=17 evals=30254) + +thread '' (1253107) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=17 evals=15299) +[ ] - extrinsic_L5_2 (traces=11 evals=22046) +[ ] - extrinsic_L5_5 (traces=16 evals=23774) +[ ] - extrinsic_L5_7 (traces=17 evals=17447) +[ ] - extrinsic_L5_6 (traces=13 evals=19296) + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253106) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=6 evals=15182) +[ ] - extrinsic_L5_9 (traces=14 evals=25808) +[ ] - extrinsic_L5_10 (traces=6 evals=23460) +[ ] - extrinsic_L5_11 (traces=6 evals=46957) +[ ] - extrinsic_L6_1 (traces=14 evals=19117) +[ ] - extrinsic_L6_2 (traces=9 evals=56412) +[ ] - extrinsic_L6_5 (traces=17 evals=14503) +[ ] - extrinsic_L6_4 (traces=17 evals=19701) +[ ] - extrinsic_L6_3 (traces=1 evals=737) +[ ] - extrinsic_L6_6 (traces=17 evals=30745) +[ ] - extrinsic_L6_8 (traces=3 evals=42544) +[ ] - extrinsic_L6_9 (traces=11 evals=18646) +[ ] - extrinsic_L6_7 (traces=15 evals=22475) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 2/94 in 8717.5s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..dc97f3f1b19a4cacbe03968a8692c77249cc7981 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,200 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_3 (traces=17 evals=23037) +[ ] - extrinsic_L0_4 (traces=16 evals=25818) +[ ] - extrinsic_L0_6 (traces=17 evals=29095) +[ ] - extrinsic_L0_2 (traces=17 evals=24653) +[ ] - extrinsic_L0_5 (traces=14 evals=32273) +[ ] - extrinsic_L0_1 (traces=14 evals=22683) +[OK ] - extrinsic_L0_10 (traces=5 evals=1892) +[ ] - extrinsic_L0_8 (traces=17 evals=22128) +[ ] - extrinsic_L0_12 (traces=17 evals=23138) +[ ] - extrinsic_L0_7 (traces=17 evals=18653) +[ ] - extrinsic_L0_11 (traces=17 evals=26073) +[ ] - extrinsic_L0_9 (traces=15 evals=32565) +[ ] - extrinsic_L0_13 (traces=11 evals=11316) + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=17 evals=27983) +[ ] - extrinsic_L0_14 (traces=11 evals=19550) +[ ] - extrinsic_L1_1 (traces=14 evals=23999) +[ ] - extrinsic_L1_2 (traces=15 evals=27992) +[ ] - extrinsic_L1_4 (traces=15 evals=23662) +[ ] - extrinsic_L2_1 (traces=11 evals=19305) +[ ] - extrinsic_L2_2 (traces=17 evals=18624) +[ ] - extrinsic_L2_3 (traces=15 evals=29908) +[ ] - extrinsic_L2_4 (traces=13 evals=30079) +[ ] - extrinsic_L2_5 (traces=11 evals=23255) +[ ] - extrinsic_L2_6 (traces=17 evals=24709) +[ ] - extrinsic_L2_7 (traces=17 evals=12691) + +thread '' (1621700) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621700) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1621700) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_8 (traces=8 evals=19010) + +thread '' (1621703) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621703) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_9 (traces=17 evals=16111) +[ ] - extrinsic_L2_12 (traces=17 evals=24077) +[ ] - extrinsic_L2_10 (traces=15 evals=30837) +[ ] - extrinsic_L2_11 (traces=14 evals=17376) + +thread '' (1621701) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621701) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_13 (traces=13 evals=33325) + +thread '' (1621702) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1621702) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1621696) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_1 (traces=11 evals=12871) +[ ] - extrinsic_L3_2 (traces=14 evals=18975) + +thread '' (1621699) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1621699) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=15 evals=21693) +[ ] - extrinsic_L3_4 (traces=13 evals=25879) +[ ] - extrinsic_L3_5 (traces=15 evals=21133) +[ ] - extrinsic_L3_6 (traces=15 evals=14158) +[ ] - extrinsic_L3_9 (traces=17 evals=21855) +[ ] - extrinsic_L3_7 (traces=8 evals=14209) +[ ] - extrinsic_L3_8 (traces=13 evals=26062) + +thread '' (1621703) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1621703) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_10 (traces=14 evals=23036) +[ ] - extrinsic_L3_11 (traces=13 evals=37020) +[ ] - extrinsic_L3_12 (traces=14 evals=26671) diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..a0914671065cc73295792b2e4196ba14cff85ba7 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 18 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s43/train.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/train.log new file mode 100644 index 0000000000000000000000000000000000000000..9936a076cf263b79d4dd87e99933f28179aaba8d --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s43/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070920-oypnpj4h +[2026-06-29T07:09:16.694659] Seeded RNGs with seed=43 +[2026-06-29T07:09:16.694948] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-29T07:09:20.082068] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json + 526 training examples loaded. + +============================================================ +[2026-06-29T07:09:20.083284] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 526 -> 526 unique examples + Epoch 1/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 18 total steps, 526 unique examples (batch_size=64) +[2026-06-29T07:09:23.943072] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:23.949543] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s43/2026-06-29_07-09-16/summary.json + 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not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6856, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type p1@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 35, + "evals_used": 172, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro." + ] + } + ], + "problem": "extrinsic_L0_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 24378, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 592, + "actions": [ + "intro.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "c em", + "=> (em goal0).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 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-> (or 'P 'Q)])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]).", + "a or_e", + "=> [false -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]; [(not false) -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]))].", + "intro.", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 579, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal2).", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false).", + "c em", + "=> (em p@type).", + "a x", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) false) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (and (and (and (and (and (and false 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(iff 'P 'Q)]).", + "a x2", + "=> false.", + "c x2", + "=> (x2 and_er@type and_i@type x1 and_i).", + "c x1", + "=> (x1 and_er@type and_i@type p4).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c and_el", + "=> (and_el and_er@type and_el@type p1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "c p7", + "=> (p7 goal and_i@type p4).", + "c p8", + "=> (p8 iff_i@type em@type iff_i em).", + "c p8", + "=> (p8 p1@type and_i@type p1 p8).", + "c p5", + "=> (p5 p4@type iff_i@type p4 iff_i).", + "a p2", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, 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em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7123, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[false -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> false] -> false]]]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[false -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] false); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [false -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 368, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso and_er).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 597, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [false -> ('P : prop) -> 'P])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (not [false -> ('P : prop) -> 'P]))]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not (not [false -> ('P : prop) -> 'P]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 623, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a x", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)))].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)))]]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) false)))]].", + "intro.", + "a exfalso", + "=> false.", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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-> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "c x", + "=> (x goal p2@type@2 and_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x1 exfalso).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4457, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el exfalso@type or_il@type p3).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x2", + "=> (x2 not_e@type p@type x0 p).", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_i@type or_il@type x2 or_il).", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a p4", + "=> false.", + "c em", + "=> (em goal2).", + "c x2", + "=> (x2 exfalso@type p2@type exfalso p2).", + "c x2", + "=> (x2 iff_el@type p0@type iff_el p0).", + "a p4", + "=> false.", + "a p4", + "=> false.", + "c x2", + "=> (x2 and_er@type em@type and_er em)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> false]; [(not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> false]]; [(not (or [('P : prop) -> 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])); (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]).", + "c x", + "=> (x em@type p5@type@2 em).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false]].", + "c x", + "=> (x p4@type p5@type@2 p4).", + "c em", + "=> (em goal16).", + "c x", + "=> (x p4@type p1@type@2 p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 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'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c x", + "=> (x not_i@type goal not_i or_ir).", + "c em", + "=> (em p@type).", + "c p0", + "=> (p0 and_er@type and_i@type x).", + "c em", + "=> (em p5@type).", + "c p0", + "=> (p0 false exfalso@type exfalso).", + "c x", + "=> (x p7@type p5@type p7 p5).", + "c and_el", + "=> (and_el p7@type p5@type p9).", + "c p0", + "=> (p0 p5@type not_e@type not_e).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [false -> ('P : prop) -> 'P] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(or [false -> ('P : prop) -> 'P] [false -> ('P 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]])]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 449, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c x1", + "=> (x1 iff_i@type exfalso@type exfalso).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 goal9 exfalso@type exfalso).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]; [[false -> ('P : prop) -> 'P] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or (not [('P : prop) -> (or 'P (not 'P))]) [false -> ('P : prop) -> 'P]))]]]].", + "c x2", + "=> (x2 x1).", + "c x2", + "=> (x2 or_ir).", + "c x1", + "=> (x1 p3@type goal4 x2).", + "c em", + "=> (em goal17).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 285, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 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exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]) -> false].", + "c em", + "=> (em false).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (iff false [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (iff false [false -> ('P : prop) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (iff false [false -> ('P : prop) -> 'P])].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> (iff false [false -> ('P : prop) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]) -> (iff false [false -> ('P : prop) -> 'P])].", + "a x", + "=> (iff (iff false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1416, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal not_e@type iff_er).", + "c x", + "=> (x iff_i@type or_e@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type or_e@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2213, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x goal goal16 iff_er).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]] (or false (not false))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) 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'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])); (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]]].", + "a or_e", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]]]]; [(not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]))]]]].", + "c x2", + "=> (x2 and_i).", + "c x1", + "=> (x1 p0@type@2).", + "c x1", + "=> (x1 goal16).", + "c em", + "=> (em goal20).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em false).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1423, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal or_e@type iff_i).", + "c x", + "=> (x iff_i@type or_ir@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7376, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]); [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])])].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 5183, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 iff_i).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type iff_i@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type x2 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L0_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19261, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", 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-> (and 'P 'Q) -> 'Q])] -> (not (not (not [('A : prop) -> (or 'A (not 'A))])))]; [(not [[('A : prop) -> (or 'A (not 'A))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> (not (not (not [('A : prop) -> (or 'A (not 'A))])))].", + "intro.", + "a not_i", + "=> [(not (not [('A : prop) -> (or 'A (not 'A))])) -> false].", + "a exfalso", + "=> .", + "intro.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 565, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('A : prop) -> (or 'A (not 'A))] false).", + "a and_i", + "=> [('A : prop) -> (or 'A (not 'A))]; false.", + "a x", + "=> (and false [('A : prop) -> (or 'A (not 'A))]).", + "a x", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and 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(and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))).", + "a x", + "=> (and (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)))))))).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)) -> (and (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] 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-> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))) [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)) -> (and (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))))]) false).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))) [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)) -> (and (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))))]); false.", + "a and_i", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))); [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false)) -> (and (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))) (and [('P : prop) -> (or 'P (not 'P))] (and [('A : prop) -> (or 'A (not 'A))] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] false))))))))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false) -> false]; [(not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + 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-> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) 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or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]].", + "a x", + "=> (iff [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a iff_i", + "=> [[(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false]].", + "a x", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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-> 'R])]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "c em", + "=> (em goal9).", + "a or_il", + "=> .", + "a x1", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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-> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false]; [(not [('A : prop) -> ['A -> false] -> (not 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> false]; [(not [('A : prop) -> ['A -> false] -> (not 'A)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1457, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P 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or_e", + "=> [[('A : prop) -> ['A -> false] -> (not 'A)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c x", + "=> (x goal p2@type@2 not_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [false -> [false -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [false -> [false -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4575, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[x -> false] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[x -> false] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 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-> 'C] -> ['B -> 'C] -> 'C] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] -> false]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2265, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L1_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19796, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false]); [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (not [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false])]; [(not [false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]) -> (not [[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false])].", + "intro.", + "a not_i", + "=> [[[false -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 612, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a 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em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]].", + "a x0", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1184, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not x)].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p4@type iff_el).", + "a exfalso", + "=> false.", + "a x1", + "=> (and [x -> false] false).", + "a x1", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [x -> false] false)).", + "c em", + "=> (em goal13).", + "a and_i", + "=> (and [x -> false] false).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (and [x -> false] false)]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (and [x -> false] false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('B : prop) -> [(not x) -> [x -> 'B]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('B : prop) -> [(not x) -> [x -> 'B]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) 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not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "intro.", + "c em", + "=> (em goal8).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1662, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> 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('B : prop) -> [(not 'A) -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]])) -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x goal iff_er@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + 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-> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2006, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em 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prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])); (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]).", + "c em", + "=> (em goal11).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1543, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c p5", + "=> (p5 not_i).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]); [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]); [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4269, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il 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: prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em 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(and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p0@type@2).", + "intro.", + "a x0", + "=> (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x0", + "=> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]].", + "a x0", + "=> (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "c em", + "=> (em goal23).", + "a x0", + "=> (and (and [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 456, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 657, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x0", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a x0", + "=> (and (and false (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) x).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (and (and false (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) x)]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (and (and false (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) x)].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2345, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c x1", + "=> (x1 or_e@type iff_i@type or_e iff_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + 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false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])].", + "a p4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[false -> ('P : prop) -> 'P] -> (or (not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (or (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3123, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x", + "=> (x p@type@2 goal8).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + } + ], + "problem": "extrinsic_L1_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 27114, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 248, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [false -> false]]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> [false -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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-> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x", + "=> (x goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]; [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2058, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [false -> [false -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> (and 'B x)]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 555, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c x0", + "=> (x0 p3@type).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 em@type).", + "c x1", + "=> (x1 em).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false." + ] + }, + { + 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prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em p0@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "a x1", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]) -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]].", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]).", + "a x2", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]]]] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] -> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> (and x 'B) -> (and 'B x)]])) (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))])).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]; [(not [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] 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-> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x0", + "=> (x0 goal11).", + "c x0", + "=> (x0 em@type).", + "c x0", + "=> 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('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]] -> false]].", + "c x1", + "=> (x1 goal p1@type p1).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4328, + "actions": [ + "c em", + "=> (em 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'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) 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false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : 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(iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", 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[('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c x", + "=> (x iff_i@type not_e@type iff_i not_e)." + ] + } + ], + "problem": "extrinsic_L2_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 18265, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", 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: prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))).", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))))))).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))]; [(not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))].", + "a x", + "=> (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) [(and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) [(and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))]) false).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) [(and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))]); false.", + "a and_i", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false); [(and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)) (and (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false)))) (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) false))))))))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) false) -> false]; [(not (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] false) false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : 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-> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]) [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]); [(not [(or [('P : prop) -> ('Q : prop) -> 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-> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 632, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['B -> 'C] -> [x -> 'C]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]].", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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"=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]]))); (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])).", + "a not_i", + "=> [(not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em em@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + 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'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "c x0", + "=> (x0 and_el@type em@type and_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not 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: prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em p3@type@2).", + "a x", + "=> (and [false -> ('P : prop) -> 'P] false).", + "a x", + "=> (and [false -> ('P : prop) -> 'P] (and [false -> ('P : prop) -> 'P] false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 418, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a exfalso", + "=> .", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [false -> [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 926, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_el@type p3@type iff_el p3).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_el@type p3@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2911, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P 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false].", + "c em", + "=> (em goal8).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p8@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p5@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "intro.", + "a x1", + "=> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2084, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 610, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x1", + "=> (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a and_i", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]] (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]]; (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]]).", + "a exfalso", + "=> false.", + "a x", + "=> (not (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]])); (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])])]]).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x1", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 707, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1945, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> 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'P]]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 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[false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P])))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 459, + "actions": [ + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 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-> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> false] [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 52, + "evals_used": 2113, + "actions": [ + "c em", + 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x x) -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x x) -> x]]]].", + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[false -> ('P : prop) -> 'P] -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (iff [false -> ('P : prop) -> 'P] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x x) -> x]]]); [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x x) -> x]]].", + "a x2", + "=> [[[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x x) -> x]]] -> false].", + "c em", + "=> (em p2@type).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x3", + "=> (x3 exfalso).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 390, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [false -> ('P : prop) -> 'P]) -> 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false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2074, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal16 p3@type p3).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(iff (or x x) x) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not (iff (or x x) x)) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c x1", + "=> (x1 p@type@2 p1@type p1).", + 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false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "a not_i", + "=> [[false -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 311, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : 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-> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "c em", + "=> (em p2@type).", + "intro.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "c x2", + "=> (x2 x false x0).", + "c em", + "=> (em p4@type@2).", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('A : prop) -> (iff (and 'A 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (or [('A : prop) -> (iff (and 'A false) false)] (not [('A : prop) -> (iff (and 'A false) false)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]))))].", + "c em", + "=> (em goal19)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c em", + "=> (em goal11).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p3@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[[('A : prop) -> (iff (and 'A false) false)] -> false] -> [x -> false]]; [(not [[('A : prop) -> (iff (and 'A false) false)] -> false]) -> [x -> false]].", + "intro.", + "c em", + "=> (em p5@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 470, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(and x false) -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]].", + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [(and x false) -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a iff_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4369, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]).", + "a p8", + "=> (and (and (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 418, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 false p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x goal).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6156, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A false) false)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A false) false)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + 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(not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])); [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_ir", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]).", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x3", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 900, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + 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-> false] -> false]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x1", + "=> (x1 iff_el@type or_ir@type iff_el or_ir).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 405, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]); [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or (or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) (not (or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1761, + 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(or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "c x", + "=> (x goal14 and_el@type and_el).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x1 exfalso).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1329, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not false)); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> (iff 'B (and 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false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]])) -> false]].", + "a x0", + "=> (iff [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]])) -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal12).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 463, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + 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+ "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or x (not x))).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not false)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not false)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]); [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> 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false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + 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-> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff x 'B) -> (iff 'B 'C) -> (iff x 'C)]]]]].", + "c x1", + "=> (x1 or_il@type p12@type or_il p12).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p12@type p3 p12).", + "c x1", + "=> 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'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1947, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a x0", + "=> (or (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 6423, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> ['B -> [x -> 'C]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0" + ] + } + ], + "problem": "extrinsic_L3_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 11, + "evals_used": 13075, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 407, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]].", + "a or_e", + "=> [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])]; [(not false) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])] (not [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])]))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [false -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]])]) -> (not [('P : prop) -> ('Q : prop) 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])) -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_il", + "=> .", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])) -> false]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])) -> false]]]; [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])) -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 455, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : 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prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "c em", + "=> (em goal19).", + "c x", + "=> (x not_i@type x3 not_i).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 not_i@type x3 not_i).", + "c x2", + "=> (x2 not_i@type x3 not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1386, + "actions": [ + "a exfalso", + "=> false.", + "a 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false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 41, + "evals_used": 1244, + "actions": [ + "c em", + "=> (em 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-> (or (not false) [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not false) [false -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not false) [false -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not false) [false -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not false) [false -> 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-> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + 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-> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) 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prop) -> [(and x 'B) -> 'C] -> [x -> ['B -> 'C]]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p)." + ] + } + ], + "problem": "extrinsic_L3_3" + }, + { + "solved": 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-> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [false -> ('P : prop) -> 'P]))]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [false -> ('P : prop) -> 'P]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal6).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 723, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : 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'Q]))))]].", + "a x0", + "=> (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]).", + "c em", + "=> (em goal18).", + "a x0", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 461, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 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'P 'Q)]) -> false].", + "intro.", + "a x1", + "=> (and [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a x1", + "=> (and (not [('P : prop) -> (or 'P (not 'P))]) false).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 724, + "actions": [ + "intro.", + "c em", + "=> (em 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x0", + "=> (x0 goal8).", + "c x0", + "=> (x0 x).", + "c x0", + "=> (x0 p8@type).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2).", + "c x0", + "=> (x0 p4@type).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 482, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", 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'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> 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prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type 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false] -> false])).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]].", + "c x0", + "=> (x0 p@type iff_i@type iff_i).", + "c x0", + "=> (x0 p@type iff_el@type iff_el).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]])].", + "c x0", + "=> (x0 iff_i@type or_e@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1462, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + 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-> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> 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-> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P 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(not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and (or [('A : prop) -> ('B : prop) 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-> ['B -> (not 'A)]]) -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and (or [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])) (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and (or [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])) (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (and (or [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])) (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "intro.", + "c em", + "=> (em or_e@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 545, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a not_i", + "=> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) 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(and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))); (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x0", + "=> (and (not (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))." + ] + } + ], + "problem": "extrinsic_L3_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 19482, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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+ "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) 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false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 516, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not false) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not false) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not false) -> [('B : prop) -> ('C : prop) -> 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-> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]].", + "a x1", + "=> (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]).", + "c em", + "=> (em goal18).", + "a x1", + "=> (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]])).", + "a x1", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]))).", + "a and_i", + "=> (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not x0)))]]) (and [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> 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prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> false]].", + "c x", + "=> (x p5@type or_ir@type p5).", + "c em", + "=> (em goal16).", + "c x", + "=> (x p4@type goal16 p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2028, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[('P : prop) -> 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-> 'R] -> 'R]) [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (or 'P (not 'P))] -> false])).", + "a x0", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [('P : prop) -> (or 'P (not 'P))] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> (or 'P (not 'P))] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a x0", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> (not 'P) -> 'P -> false] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('P : prop) -> (not 'P) -> 'P -> false] false))]; [(not [('P : prop) 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false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]); [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]); [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]); [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))].", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a p4", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))])); [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))]; [(not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> (or [('P : prop) -> (or 'P (not 'P))] (not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]))].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em 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-> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + 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prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "a x", + "=> (or [[[false -> ('P : prop) -> 'P] -> false] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[[false -> ('P : prop) -> 'P] -> false] -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[false -> ('P : prop) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x" + ] + } + ], + 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-> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + 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-> (not (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]))].", + "intro.", + "a not_i", + "=> [(not [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5204, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] 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p7@type p8@type p8).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 goal0 p9@type p9).", + "c x0", + "=> (x0 p3@type p3@type p3).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p8@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2109, + "actions": [ + "c em", + "=> 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('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[(not [false -> ('P : prop) -> 'P]) -> false] -> false]; [(not [(not [false -> ('P : prop) -> 'P]) -> false]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c p8", + "=> (p8 goal p0@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3134, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c x3", + "=> (x3 and_i@type p0@type x3 p0).", + "c and_el", + "=> (and_el and_i@type p0@type p2).", + "c p3", + "=> (p3 or_il@type em@type or_il em).", + "c x3", + "=> (x3 and_er@type and_i@type and_er and_i).", + "c em", + "=> (em p4@type).", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 p0@type not_e@type p0 x1).", + "c x3", + "=> (x3 iff_er@type not_e@type iff_er x).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : 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false]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7034, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> false].", + "a x", + "=> (or (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])].", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] [[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false]); [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[[(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (or (not x) (not 'B)) -> (not (and x 'B))]].", + "intro.", + 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[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 55, + "evals_used": 2419, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", 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not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a 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-> 'R]))).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x", + "=> (x iff_er@type exfalso@type exfalso).", + "c x", + "=> (x p3@type@2 em@type em).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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-> 'P]) (not (not [false -> ('P : prop) -> 'P]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B 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false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", 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-> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 494, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (or [('P : 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-> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false 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prop) -> 'P]))) -> false].", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]).", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false])).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (and [('P : prop) -> (or 'P (not 'P))] (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 511, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> false].", + "c em", + "=> (em p1@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4518, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c and_er", + "=> (and_er em@type iff_i@type p4).", + "c x2", + "=> (x2 p@type and_i@type p x).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p5@type and_el@type p5 and_el).", + "a p8", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7331, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> false]; [(not [false -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> false] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> false] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + } + ], + "problem": "extrinsic_L3_13" + }, + { + "solved": false, + "greedy_solved": 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false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_er@type p3@type iff_er p3).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em 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(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) 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-> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x0", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em goal10).", + "a x0", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a and_i", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 52, + "evals_used": 10588, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a iff_i", + "=> [(or x (and x x2)) -> x]; [x -> (or x (and x x2))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p@type p2@type p2).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir x1).", + "c x1", + "=> (x1 not_i@type p5@type not_i p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false iff_el@type iff_el).", + "c x1", + "=> (x1 and_er@type p11@type and_er p11).", + "c p9", + "=> (p9 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4@1@2).", + "c p4", + "=> (p4 x p1@type p1).", + "c p4", + "=> (p4 p1@type p0@type p0)." + ] + } + ], + "problem": "extrinsic_L3_15" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 29449, + "solution_actions": null, + "traces": [ + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "c em", + "=> (em or_e@type).", + "intro.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false]) (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal14).", + "a x", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false]) (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])] [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))])); (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> (or 'P (not 'P))]))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x and_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "a exfalso", + "=> .", + "a or_e", + "=> 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))); (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (not (not x))) -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p0@type p4 p7).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (not (not x))) -> (not x)]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 4936, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or (not x) (not (not x)))); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(or (not x) (not (not x))) -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))).", + "a x0", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [[('P : prop) -> (or 'P (not 'P))] -> false]); [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [[[('P : prop) -> (or 'P (not 'P))] -> false] -> 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"=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4271, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 569, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x1", + "=> (and false (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (and false (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (and false (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p1@type@2).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (and false (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]]; [(not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (and false (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2258, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> (and x (or 'B 'C)) -> (or (and x 'B) (and x 'C))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 587, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x1", + "=> (x1 p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 647, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]]." + ] + }, + { + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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(and [('P : prop) -> ['P -> false] -> (not 'P)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (not (or [('P : prop) -> ('Q : prop) 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false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x1", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] false).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 453, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]].", + "intro.", + "c em", + "=> (em goal8).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 483, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 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(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[false -> ('P : prop) -> 'P] -> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[false -> ('P : prop) -> 'P] -> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) false)]].", + "intro.", + "c em", + "=> (em iff_er@type).", + "a x1", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> 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(not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 556, + "actions": [ + "a exfalso", + "=> false.", + "a 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prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c em", + "=> (em goal8).", + "c em", + "=> (em and_el@type).", + "intro.", + "a 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'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> false; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x", + "=> (and false [false -> ('P : prop) -> 'P]).", + "a x", + "=> (and (and false [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a x", + "=> (and (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal13).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> (and (and (and (and (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> (not 'P) -> 'P -> false]) (and 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: prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x1", + "=> (x1 not_e@type or_il@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 688, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x1", + "=> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))].", + "c em", + "=> (em goal11@1).", + "c em", + "=> (em p0@type).", + "a x1", + "=> (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])).", + "a or_ir", + "=> (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]).", + "a and_i", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "a x1", + "=> (or (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]) (and (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false])).", + "a or_il", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]).", + "a x1", + "=> (or (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false])) (and (not (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]))) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]))).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (and (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false])) false) (and (not (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]))) false)).", + "a x1", + "=> (or (and [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false] (or (and (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false])) false) (and (not (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]))) false))) (and (not [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]) (or (and (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false])) false) (and (not (and (or (and [[('P : prop) -> (or 'P (not 'P))] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]) (and (not [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))])) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]))) false)))).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 397, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false] (not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B])))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2156, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 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-> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [false -> ('P : prop) -> 'P])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> ('P : prop) -> 'P]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> ('P : prop) -> 'P]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 543, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]; [(not false) -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]].", + "a or_e", + "=> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]; [(not false) -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [('B : prop) -> (or (and x 'B) (and (not x) 'B)) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a 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not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type@2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c x", + "=> (x not_e@type x1 x).", + "c em", + "=> (em goal)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 417, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 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-> ('P : prop) -> 'P] -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> [[false -> ('P : prop) -> 'P] -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> [[false -> ('P : prop) -> 'P] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 49, + "evals_used": 4823, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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: prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] false).", + "a iff_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> false]; [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))]]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal19).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))).", + "c em", + "=> (em p2@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "c iff_el", + "=> (iff_el iff_er@type p6@type@2 p6)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5213, + "actions": [ + "intro.", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not x)); (not x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [(or (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not [('P : prop) -> 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> (not (not x))]]]].", + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (iff [x -> (not (not x))] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "a x3", + "=> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a iff_i", + "=> [false -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c em", + "=> (em and_i@type).", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false)].", + "a x0", + "=> (iff (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x2", + "=> (x2 p6@type@2).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (iff (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> (iff (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x0", + "=> (iff (iff (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 x).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 528, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A (not (not 'A)))]].", + "intro.", + "intro.", + "a iff_i", + "=> [x0 -> (not (not x0))]; [(not (not x0)) -> x0].", + "c em", + "=> (em and_el@type).", + "a or_e", + 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-> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [false -> ('P : prop) -> 'P]))); (not (not [false -> ('P : prop) -> 'P])).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c x2", + "=> (x2 p@type or_ir@type p or_ir).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]).", + "a p8", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])])]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not false); false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a not_i", + "=> [(or false [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 633, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) 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false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x2", + "=> false.", + "a x", + "=> (not (not [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]])); (not [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> (not [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]])]]).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])); (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]))]; [(not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]) -> (not (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type x2 p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c x0", + "=> (x0 em@type not_i@type em not_i).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 570, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]); [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3196, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type not_e@type p0 not_e).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p0@type not_e@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1271, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "c x1", + "=> (x1 p1@type p4@type p1 p4).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 532, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[false -> 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-> [(not 'B) -> 'A]] (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em p@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 898, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 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false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [(not x) -> 'B] -> [(not 'B) -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [[('A : prop) -> ('B : 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false])] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 374, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c not_e", + "=> (not_e and_er@type x and_er).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> .", + "a exfalso", + 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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-> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 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prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a x", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em goal11).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]); [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x", + "=> false.", + "c em", + "=> (em p4@type).", + "a x1", + "=> (and false (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]])))).", + "a x1", + "=> (and (and false (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]])))) (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))])).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3276, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c iff_er", + "=> (iff_er p6@type@1 p6@type@2 p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type goal).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]); [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]); [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9121, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "c x0", + "=> (x0 not_e@type and_er@type x2 and_er).", + "c and_el", + "=> (and_el not_e@type and_er@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 567, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "c x0", + "=> (x0 p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "intro.", + "intro.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 45, + "evals_used": 3253, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2 not_e@type not_e).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c x", + "=> (x p@type@2 or_e@type or_e).", + "c x", + "=> (x goal2 p1@type p1).", + "a exfalso", + "=> false.", + "c x", + "=> (x p2@type@2 p6@type p6)." + ] + } + ], + "problem": "extrinsic_L4_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 16940, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 806, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x p0@type p@type p0 p).", + "c and_er", + "=> (and_er p0@type p@type p5).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em not_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 554, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and false [false -> ('P : prop) -> 'P]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [false -> ('P : prop) -> 'P]).", + "a x", + "=> (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])).", + "c em", + "=> (em goal).", + "a x", + "=> (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p@type).", + "a x", + "=> (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false).", + "a x", + "=> (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x", + "=> (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]).", + "a x", + "=> (and (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> (and (and (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> (and (and (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]))) -> (and (and (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> (and (and (and (and (and (and (and false (and (and false [false -> ('P : prop) -> 'P]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) [('P : prop) -> (or 'P (not 'P))]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em p@type@2).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> .", + "c em", + "=> (em goal10)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> false].", + "c em", + "=> (em goal11).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "c x2", + "=> (x2 x0).", + "c not_e", + "=> (not_e or_ir@type p4 or_ir).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 x0).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 494, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p5@type).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 492, + "actions": [ + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))).", + "a not_i", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]])); (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]] -> (not (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]))]; [(not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]) -> (not (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x [x -> 'B])]]]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "c em", + "=> (em p@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8824, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 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: prop) -> (not 'P) -> 'P -> false]]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]]]; [[(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]]]]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]])] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ['P -> false] -> (not 'P)]) [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (not 'P) -> 'P -> false]]))]]]].", + "c x2", + "=> (x2 p@type exfalso@type p exfalso).", + "c x2", + "=> (x2 iff_er@type p1@type iff_er p1).", + "c x2", + "=> (x2 p3@type p6@type p3 p6).", + "c x1", + "=> (x1 goal16 p8@type).", + "c em", + "=> (em x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 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or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1983, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x [x -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1877, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "a or_ir", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 p0@type@2).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 471, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a x0", + "=> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]].", + "intro.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> (and (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 392, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : 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['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not false); false.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not false)); (not false).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em exfalso@type)." + ] + }, + { + "mode": "sample", + 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false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c x1", + "=> (x1 iff_i@type iff_el@type iff_el).", + "intro.", + "c x2", + "=> (x2 goal13).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x3", + "=> (x3 p1@type).", + "a or_ir", + "=> .", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 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[('P : prop) -> (not 'P) -> 'P -> false]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false])))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false])))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> 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false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [(or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]); [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]); [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [(or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]] (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]] -> (or (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1330, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (not (not [false -> ('P : prop) -> 'P])) (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))); [(not (not [false -> ('P : prop) -> 'P])) -> false]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_il", + "=> (not (not [false -> ('P : prop) -> 'P])).", + "c em", + "=> (em or_ir@type).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x1", + "=> (or [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not false)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : 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-> false] -> false].", + "c x1", + "=> (x1 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10162, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal5).", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 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'P 'Q)])]; [(or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))) -> (or [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> 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'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))) -> (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (not (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))))]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (or (or (or false [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (or 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-> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false] -> false]; [(not [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]) -> false].", + "intro.", + "a x2", + "=> .", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1317, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) 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exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "c x1", + "=> (x1 p2@type iff_el@type p2 iff_el).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em 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('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em x).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]); [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x1", + "=> (x1 and_i).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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"=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e not_i@type x1 not_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 333, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [[[x -> 'B] -> x] -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 558, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))); (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or (not (not [('P : prop) -> (or 'P (not 'P))])) (not (not (not [('P : prop) -> (or 'P (not 'P))]))))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (or (not (not [('P : prop) -> (or 'P (not 'P))])) (not (not (not [('P : prop) -> (or 'P (not 'P))])))))]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not (or (not (not [('P : prop) -> (or 'P (not 'P))])) (not (not (not [('P : prop) -> (or 'P (not 'P))])))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 446, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not 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-> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))))]].", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))))]]).", + "c em", + "=> (em goal18).", + "a x", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))))]]))." + ] + }, + { + "mode": "sample", 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goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 368, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [false -> ('P : prop) -> 'P]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "c em", + "=> (em goal7).", + "a x0", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p0@type@2).", + "a x0", + "=> false.", + "a x0", + "=> false.", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2587, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type or_ir).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x1", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type or_e@type or_e).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a or_e", + "=> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 624, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]; false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a x", + "=> (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]).", + "a x", + "=> (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)].", + "intro.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]) (and (and [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]])) false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 384, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 5034, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x", + "=> (x or_e@type goal9 or_e).", + "c x", + "=> (x or_ir@type not_i@type or_ir).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em goal4).", + "c em", + "=> (em and_el@type).", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em p2@type@2).", + "a x", + "=> .", + "c x", + "=> (x and_er@type p7@type@2 and_er).", + "c x", + "=> (x exfalso@type and_er@type exfalso).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0" + ] + } + ], + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 8, + "evals_used": 25223, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + 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'P (not 'P))]))]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))])))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]) -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))])))].", + "intro.", + "c x", + "=> (x iff_er).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a x0", + "=> (and (not [false -> ('P : prop) -> 'P]) (not [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [false -> ('P : prop) -> 'P]) (not [false -> ('P : prop) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (not [false -> ('P : 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[('P : prop) -> ['P -> false] -> (not 'P)])) -> false])).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [false -> ('P : prop) -> 'P] (and (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or (not 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false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]; [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) 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"a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal8).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [false -> false]].", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))].", + "a x", + "=> (and [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> (and (and (and (and (and (and (and false (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (and false (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7739, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a 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-> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]]].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [(or (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))) -> false]; [(not (or (not (or 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prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))); (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 499, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em or_e@type).", + "intro.", + "c em", + "=> (em goal2).", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a x0", + "=> (iff (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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(iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type iff_i@type iff_i).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[false -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[false -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false]]].", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 419, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e" + ] + } + ], + "problem": "extrinsic_L5_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 3, + "evals_used": 26073, + "solution_actions": 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exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "c x", + "=> (x p3@type@2 p3@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 45, + "evals_used": 24150, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false].", + "intro.", + "c x", + "=> (x or_e@type and_el@type).", + "a not_e", + "=> (not (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c x", + "=> (x exfalso@type goal1).", + "c x", + "=> (x em@type em@type).", + "c iff_el", + "=> (iff_el p0@type@1 p0@type@2 p0).", + "c x", + "=> (x p1@type iff_i@type).", + "c iff_el", + "=> (iff_el p3@type@1 p3@type@2 p3).", + "c iff_el", + "=> (iff_el p1@type@1 p1@type@2 p1).", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type@2).", + "c x", + "=> (x or_ir@type and_i@type).", + "c em", + "=> (em p8@type@1).", + "c x", + "=> (x false p4@type).", + "c x", + "=> (x p10@type@2 p10@type@2@2).", + "c x", + "=> (x exfalso@type or_ir@type).", + "c x", + "=> (x p11@type@2@2 p8@type).", + "c em", + "=> (em p3@type@1).", + "a not_i", + "=> [(iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p@type@2@2 p10@type@1@1)." + ] + } + ], + "problem": "extrinsic_L5_7" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 22558, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + 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-> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a 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-> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]))) -> false].", + "c x", + "=> (x not_i@type or_ir@type).", + "intro.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 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and_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + 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and_i@type or_ir@type p11 p0).", + "c x", + "=> (x and_i@type and_er@type p11 and_er).", + "c x", + "=> (x em@type p14@type em p14).", + "c p11", + "=> (p11 and_i@type p6@type p11 p6).", + "c p0", + "=> (p0 and_el@type iff_i@type iff_i).", + "a not_e", + "=> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]) (or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c p11", + "=> (p11 p3@type and_er@type p3 and_er).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1650, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + 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(not (and (not x) (not x0))); (and (not x) (not x0)).", + "c x1", + "=> (x1 exfalso@type em@type exfalso em).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not (and (not x) (not x0)))]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> (not (and (not x) (not x0)))].", + "c and_er", + "=> (and_er exfalso@type em@type p4).", + "c p5", + "=> (p5 goal9).", + "c em", + "=> (em p6@type@2).", + "c p5", + "=> (p5 p2@type).", + "c p5", + "=> (p5 iff_el@type).", + "intro.", + "c x1", + "=> (x1 p1@type em@type p1 p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 388, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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false]; [(not (not [false -> ('P : prop) -> 'P])) -> false].", + "a x0", + "=> false.", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 13254, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))].", + "c em", + "=> (em iff_i@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false].", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not (not false)); (not false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x goal7 em@type).", + "c em", + "=> (em goal1).", + "c x", + "=> (x p7@type@2 p6@type@2).", + "c iff_el", + "=> (iff_el p8@type@1 p8@type@2 p8).", + "c x", + "=> (x p2@type@2 p6@type@2).", + "c x", + "=> (x p6@type goal).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p6@type@1 p6@type@2 p6).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p10@type@1 p10@type@2 p10).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c iff_er", + "=> (iff_er p11@type@1 p11@type@2 p11).", + "c x", + "=> (x p6@type@2 p5@type@2).", + "intro." + ] + } + ], + "problem": "extrinsic_L5_9" + }, + { + "solved": false, + "greedy_solved": false, + 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'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> 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[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]].", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] false).", + "a and_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]; false.", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]).", + "a x1", + "=> (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a x1", + "=> (and (and false (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) [false -> ('P : prop) -> 'P]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3512, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x goal3 p0@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 506, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 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(not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> false].", + "intro.", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c x0", + "=> (x0 p2@type false)." + ] + } + ], + "problem": "extrinsic_L5_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + 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-> [x -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])])]; [(or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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(iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or [x -> 'B] ['B -> 'C])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> 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-> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x1", + "=> 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-> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em x).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "c x4", + "=> (x4 not_i@type em@type not_i).", + "c x3", + "=> (x3 p4@type x p4).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em goal).", + "a x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a iff_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 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-> (or 'P 'Q)] -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em and_el@type).", + "intro.", + "a x", + "=> (iff false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (iff false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p3@type@2)." + ] + } + ], + "problem": "extrinsic_L5_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 24602, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 359, + "actions": [ + "c em", + "=> (em 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[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal1).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "c em", + "=> (em goal6).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> (iff 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not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> 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-> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ['P -> false] -> 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-> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] 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[false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4523, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : 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-> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) false); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]; [false -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : 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-> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff 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(iff x (iff 'B 'C)) (iff (iff x 'B) 'C))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + 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(not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or x (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))); [x -> false]; [(or [('P : prop) 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-> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x", + "=> (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])); [(not [false -> ('P : prop) -> 'P]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (or 'P (not 'P))])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or 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-> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a x1", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 538, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a x0", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "a x1", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a iff_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "c em", + "=> (em goal19).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p3@type@2).", + "a not_i" + ] + 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + 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-> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6728, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em 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exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", 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-> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..c531a5de2d6e44d3d9f0de2d4a0478695875310e --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,917 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253095) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (x [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] or_ir or_e) false exfalso@type exfalso): parameter type (and [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) and value type (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253095) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (x [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] or_ir or_e) false exfalso@type exfalso): parameter type (and [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) and value type (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) did not unify. + +thread '' (1253095) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (x [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] or_ir or_e) p2@type p1@type p1): parameter type (and [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) and value type (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) did not unify. +[OK ] - extrinsic_L0_1 (traces=4 evals=13430) +[ ] - extrinsic_L0_4 (traces=17 evals=21622) +[ ] - extrinsic_L0_3 (traces=17 evals=24378) +[ ] - extrinsic_L0_7 (traces=17 evals=13609) +[ ] - extrinsic_L0_2 (traces=12 evals=26358) +[ ] - extrinsic_L0_5 (traces=11 evals=24137) +[ ] - extrinsic_L0_6 (traces=3 evals=10162) + +thread '' (1253093) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> (not 'A) -> 'A -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (x0 [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) not_e (em [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))): parameter type (and [('A : prop) -> (not 'A) -> 'A -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) and value type (and [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L0_9 (traces=5 evals=16680) +[OK ] - extrinsic_L0_10 (traces=5 evals=15290) +[ ] - extrinsic_L0_8 (traces=17 evals=17274) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_11 (traces=13 evals=23431) +[ ] - extrinsic_L0_13 (traces=15 evals=21905) +[ ] - extrinsic_L0_12 (traces=17 evals=19261) +[ ] - extrinsic_L0_14 (traces=17 evals=21566) +[ ] - extrinsic_L1_1 (traces=12 evals=22490) +[ ] - extrinsic_L1_2 (traces=17 evals=19796) +[ ] - extrinsic_L2_2 (traces=17 evals=21358) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=14 evals=16620) +[ ] - extrinsic_L2_1 (traces=17 evals=27114) +[ ] - extrinsic_L1_4 (traces=11 evals=18177) +[ ] - extrinsic_L2_3 (traces=17 evals=18265) +[ ] - extrinsic_L2_4 (traces=9 evals=17950) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_5 (traces=17 evals=19716) +[ ] - extrinsic_L2_8 (traces=17 evals=19248) +[ ] - extrinsic_L2_6 (traces=11 evals=20776) +[ ] - extrinsic_L2_7 (traces=15 evals=25145) +[ ] - extrinsic_L2_9 (traces=14 evals=30525) +[ ] - extrinsic_L2_10 (traces=14 evals=20765) +[ ] - extrinsic_L2_11 (traces=14 evals=18127) +[ ] - extrinsic_L2_12 (traces=16 evals=19239) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_13 (traces=14 evals=35403) +[ ] - extrinsic_L3_1 (traces=13 evals=14671) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=11 evals=13075) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=13 evals=17863) +[ ] - extrinsic_L3_5 (traces=17 evals=20957) +[ ] - extrinsic_L3_4 (traces=11 evals=28609) +[ ] - extrinsic_L3_6 (traces=17 evals=19482) + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=15 evals=20487) +[ ] - extrinsic_L3_8 (traces=11 evals=21271) +[ ] - extrinsic_L3_9 (traces=11 evals=21701) +[ ] - extrinsic_L3_11 (traces=17 evals=26051) +[ ] - extrinsic_L3_12 (traces=17 evals=26558) +[ ] - extrinsic_L3_10 (traces=14 evals=34792) + +thread '' (1253093) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_13 (traces=11 evals=16907) +[ ] - extrinsic_L3_14 (traces=15 evals=19843) + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_15 (traces=13 evals=25954) +[ ] - extrinsic_L3_18 (traces=17 evals=18200) +[ ] - extrinsic_L3_16 (traces=13 evals=29449) +[ ] - extrinsic_L3_17 (traces=14 evals=30401) + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253091) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253095) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=17 evals=21180) + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_21 (traces=17 evals=16164) + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=13 evals=18575) +[ ] - extrinsic_L3_22 (traces=17 evals=12441) +[ ] - extrinsic_L3_23 (traces=17 evals=20552) +[ ] - extrinsic_L3_24 (traces=11 evals=17569) +[ ] - extrinsic_L3_25 (traces=17 evals=17946) +[ ] - extrinsic_L3_26 (traces=11 evals=19688) +[ ] - extrinsic_L3_27 (traces=13 evals=21185) + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_1 (traces=17 evals=15853) + +thread '' (1253092) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=12 evals=8563) +[ ] - extrinsic_L3_29 (traces=3 evals=8597) +[ ] - extrinsic_L4_2 (traces=11 evals=28526) +[ ] - extrinsic_L4_4 (traces=17 evals=21156) +[ ] - extrinsic_L4_3 (traces=17 evals=23843) +[ ] - extrinsic_L4_6 (traces=17 evals=23230) +[ ] - extrinsic_L4_5 (traces=17 evals=31142) +[ ] - extrinsic_L4_7 (traces=17 evals=31293) +[ ] - extrinsic_L4_9 (traces=17 evals=16940) +[ ] - extrinsic_L4_8 (traces=15 evals=31427) +[ ] - extrinsic_L4_10 (traces=17 evals=33335) +[ ] - extrinsic_L4_11 (traces=16 evals=20102) +[ ] - extrinsic_L4_12 (traces=16 evals=25631) +[ ] - extrinsic_L4_13 (traces=11 evals=38750) +[ ] - extrinsic_L4_14 (traces=17 evals=25160) +[ ] - extrinsic_L5_1 (traces=9 evals=28697) +[ ] - extrinsic_L5_2 (traces=17 evals=18212) + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=17 evals=20486) + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253094) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1253088) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_3 (traces=8 evals=25223) +[ ] - extrinsic_L5_8 (traces=17 evals=22558) +[ ] - extrinsic_L5_6 (traces=17 evals=22276) +[ ] - extrinsic_L5_5 (traces=3 evals=30562) +[ ] - extrinsic_L5_7 (traces=3 evals=26073) +[ ] - extrinsic_L5_9 (traces=6 evals=28451) +[ ] - extrinsic_L5_10 (traces=17 evals=22190) +[ ] - extrinsic_L5_11 (traces=17 evals=40025) +[ ] - extrinsic_L6_1 (traces=15 evals=24602) +[ ] - extrinsic_L6_2 (traces=2 evals=40594) +[ ] - extrinsic_L6_4 (traces=17 evals=24101) +[ ] - extrinsic_L6_3 (traces=1 evals=737) +[ ] - extrinsic_L6_5 (traces=17 evals=25338) +[ ] - extrinsic_L6_7 (traces=6 evals=14051) +[ ] - extrinsic_L6_8 (traces=9 evals=46649) +[ ] - extrinsic_L6_6 (traces=2 evals=1329) +[ ] - extrinsic_L6_9 (traces=14 evals=20780) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 3/94 in 9040.5s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log new file mode 100644 index 0000000000000000000000000000000000000000..6104766fb4021964a5d8a2495eb3d93aad10eb04 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_mid.log @@ -0,0 +1,341 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. + +thread '' (1620931) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))] (x1 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))] x1 em) and_i@type goal x1 and_i): parameter type (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) and value type (and [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] [('P : prop) -> (or 'P (not 'P))]) did not unify. +[ ] - extrinsic_L0_3 (traces=17 evals=12889) +[ ] - extrinsic_L0_2 (traces=17 evals=14045) +[ ] - extrinsic_L0_4 (traces=17 evals=19955) +[ ] - extrinsic_L0_5 (traces=17 evals=29922) +[ ] - extrinsic_L0_1 (traces=17 evals=20829) +[ ] - extrinsic_L0_6 (traces=12 evals=28384) +[OK ] - extrinsic_L0_10 (traces=5 evals=11459) + +thread '' (1620936) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P] (x [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] [false -> ('P : prop) -> 'P] iff_el exfalso)): parameter type (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P]) and value type (and [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] [false -> ('P : prop) -> 'P]) did not unify. +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L0_7 (traces=17 evals=15760) + +thread '' (1620936) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (x0 [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] not_e or_e)): parameter type (and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) and value type (and [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) did not unify. +[ ] - extrinsic_L0_8 (traces=17 evals=24397) + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_9 (traces=17 evals=29253) + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620936) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (x0 [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] not_e or_e)): parameter type (and [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) and value type (and [('P : prop) -> (not 'P) -> 'P -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]) did not unify. +[ ] - extrinsic_L0_12 (traces=17 evals=20913) +[ ] - extrinsic_L0_11 (traces=17 evals=23280) +[ ] - extrinsic_L0_13 (traces=17 evals=22955) +[ ] - extrinsic_L0_14 (traces=8 evals=13694) + +thread '' (1620937) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_4 (traces=17 evals=19353) + +thread '' (1620937) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=17 evals=22267) +[ ] - extrinsic_L1_1 (traces=17 evals=31426) + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_2 (traces=7 evals=13457) + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_1 (traces=17 evals=20074) + +thread '' (1620931) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620931) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_2 (traces=17 evals=18398) +[ ] - extrinsic_L2_6 (traces=17 evals=19919) +[ ] - extrinsic_L2_3 (traces=14 evals=25424) +[ ] - extrinsic_L2_4 (traces=17 evals=25880) +[ ] - extrinsic_L2_5 (traces=8 evals=20565) +[ ] - extrinsic_L2_7 (traces=17 evals=10940) +[ ] - extrinsic_L2_9 (traces=17 evals=21137) +[ ] - extrinsic_L2_8 (traces=17 evals=16689) + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620937) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620937) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_10 (traces=17 evals=29641) +[ ] - extrinsic_L2_11 (traces=14 evals=26636) +[ ] - extrinsic_L2_12 (traces=17 evals=21443) +[ ] - extrinsic_L2_13 (traces=15 evals=19099) +[ ] - extrinsic_L3_1 (traces=13 evals=12387) +[ ] - extrinsic_L3_2 (traces=15 evals=20760) +[ ] - extrinsic_L3_5 (traces=17 evals=21373) + +thread '' (1620934) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1620934) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_3 (traces=12 evals=17370) +[ ] - extrinsic_L3_4 (traces=15 evals=32160) +[ ] - extrinsic_L3_6 (traces=12 evals=17593) + +thread '' (1620931) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620931) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=15 evals=30385) +[ ] - extrinsic_L3_8 (traces=17 evals=25293) +[ ] - extrinsic_L3_9 (traces=13 evals=20015) + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620935) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_10 (traces=17 evals=17732) +[ ] - extrinsic_L3_11 (traces=11 evals=25590) +[ ] - extrinsic_L3_12 (traces=17 evals=33463) +[ ] - extrinsic_L3_13 (traces=17 evals=23569) + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1620938) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_15 (traces=17 evals=25074) +[ ] - extrinsic_L3_14 (traces=17 evals=22209) diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..a0914671065cc73295792b2e4196ba14cff85ba7 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 18 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s44/train.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/train.log new file mode 100644 index 0000000000000000000000000000000000000000..ca00c3dcc87cd6a77f1ee443beb3460f28115a3c --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s44/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070920-ea1qh5dt +[2026-06-29T07:09:16.765067] Seeded RNGs with seed=44 +[2026-06-29T07:09:16.765281] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-29T07:09:20.150307] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json + 526 training examples loaded. + +============================================================ +[2026-06-29T07:09:20.151539] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 526 -> 526 unique examples + Epoch 1/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 18 total steps, 526 unique examples (batch_size=64) +[2026-06-29T07:09:24.057871] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:24.065259] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s44/2026-06-29_07-09-16/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 18} diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/summary.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..52cc1931bb8b46bc842a7b45c9734d0d1228f6a4 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_0_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 18 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt new file mode 100644 index 0000000000000000000000000000000000000000..0a6d82e0a5ba6e0db01287adf227b314c29112aa --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:633739f61c241b1afc4445116de990a5822e709c8108e23ce1c6ca02f697d914 +size 318254491 diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee29c7886ae9a960370c18c7dd7eef178a50e8d --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_1.pt b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_1.pt new file mode 100644 index 0000000000000000000000000000000000000000..276acf6c84ae235054ceafa0f485d174449a1870 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_1.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6d3f93c877a3d80c0a76e1341f7b3a322002cc1c99989727429f40ca10eb6cf3 +size 318283327 diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_2.pt b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_2.pt new file mode 100644 index 0000000000000000000000000000000000000000..9416994ad1b84c8e97cc167a57a83bfc20538a46 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_2.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4e8252acd5804146ffb7ac7d0b9847bc4a69e3b58cdd0a9fae3046717d91dc34 +size 318283327 diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json new file mode 100644 index 0000000000000000000000000000000000000000..709f7d357ecce28575c03399fff9751ec5d3e2da --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json @@ -0,0 +1,90690 @@ +{ + "agent_path": 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-> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]].", + "a x2", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]]]; [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]]].", + "c em", + "=> (em goal24).", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x))]; [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] x)]] -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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[('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (not [('P : prop) -> (or 'P (not 'P))]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (or 'P (not 'P))])); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9745, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and x 'B) -> x]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 and_el).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type and_el@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and x 'B) -> x]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso", + "=> false.", + "a x2", + "=> (not false); false.", + "c x0", + "=> (x0 em@type p5@type em p5).", + "c x1", + "=> (x1 p3@type p1@type p3 p1).", + "c x1", + "=> (x1 p14@type and_i@type p14 x0).", + "c x0", + "=> (x0 and_er@type not_e@type and_er not_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1734, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type or_ir).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + 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not_i", + "=> [(not (or (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))))) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))))) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not (or (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))))) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A 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'Q) -> 'P] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p2@type@2).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]]; [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal15 and_er).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4581, + 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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-> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]); [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> 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(and 'A 'B) -> 'B]) -> false]]; [(not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false]].", + "a x", + "=> (and (not (not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))) [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false]]).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (not (not (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))) [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)].", + "intro.", + "a x0", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)).", + "a x", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]) -> false] false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 478, + 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prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [false -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])].", + "c x0", + "=> (x0 or_e@type and_i@type x)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11059, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "c x0", + "=> (x0 not_e@type p2@type not_e p2).", + "c and_el", + "=> (and_el not_e@type p2@type p3).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c x1", + "=> (x1 iff_i@type or_e@type iff_i or_e).", + "c and_el", + "=> (and_el p0@type exfalso@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type goal exfalso x0).", + "c x1", + "=> (x1 exfalso@type p2@type exfalso p2).", + "c x0", + "=> (x0 and_i@type and_er@type x0 and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type goal or_ir x0).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x0", + "=> (x0 goal not_e@type and_i x2).", + "c x1", + "=> (x1 p3@type and_i@type p3 x1).", + "c x1", + "=> (x1 p13@type p13@type p13 p13).", + "c x0", + "=> (x0 and_er@type goal and_er x1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2586, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em or_ir@type).", + "a 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"a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [false -> ('P : prop) -> 'P])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 472, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) 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(iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em goal15).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 464, + "actions": [ 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L0_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 25475, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 466, + 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-> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c x", + "=> (x p0@type iff_el@type p0 iff_el).", + "c and_er", + "=> (and_er p0@type iff_el@type p5).", + "c and_el", + "=> (and_el p0@type iff_el@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x", + "=> (x or_ir@type iff_el@type or_ir p6).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 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not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])); (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))); (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])).", + "a x1", + "=> (and (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a and_i", + "=> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]] false).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]]; false.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]] (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]] (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not (not (not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)])))]]).", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x1", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2127, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x or_il@type p3@type or_il).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> false]; [(not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]) -> false].", + "c x", + "=> (x exfalso@type goal4 exfalso).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> false]]; [(or [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] (not [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false])) -> [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1545, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal em@type or_il).", + "c x", + "=> (x iff_i@type goal10 iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type p@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8148, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (not 'P) -> 'P -> false]); [false -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type goal15 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 exfalso@type goal exfalso).", + "c x0", + "=> (x0 exfalso@type p0@type@2 exfalso).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [false -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_e@type not_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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(and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]].", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]])]] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 54, + "evals_used": 3737, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> (or 'P (not 'P))] -> false]); [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "a or_ir", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p0@type).", + "intro.", + "a x0", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x1", + "=> (x1 iff_i@type).", + "intro.", + "c x2", + "=> (x2 goal15).", + "a or_e", + "=> [[('P : 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'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x0" + ] + } + ], + "problem": "extrinsic_L0_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 36828, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 466, + "actions": [ + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em exfalso@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> 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'B)]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + 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'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])]; [(not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (or [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] (not [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]))).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1420, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x goal or_ir@type or_ir).", + "c x", + "=> (x iff_i@type or_il@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type or_e@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7192, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9745, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 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[('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 or_ir).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type or_ir@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type p4 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> 'B -> (or x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x0", + "=> (x0 em@type p5@type em p5).", + "c x1", + "=> (x1 p3@type p1@type p3 p1).", + "c x1", + "=> (x1 p14@type and_i@type p14 x0).", + "c x0", + "=> (x0 and_er@type not_e@type and_er not_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 42, + "evals_used": 3061, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or x [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P 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(not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_ir" + ] + } + ], + "problem": "extrinsic_L0_6" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 25870, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 365, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a not_e", + 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a x1", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])].", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (not 'P) -> 'P -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])]].", + "a x1", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "c x4", + "=> (x4 x2).", + "c x4", + "=> (x4 x).", + "c x4", + "=> (x4 not_e).", + "a x1", + "=> (or (or [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])])) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]])])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]].", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 380, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1477, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]]); [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x goal or_ir@type iff_el).", + "c x", + "=> (x iff_i@type and_er@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1873, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "c x0", + "=> (x0 iff_i@type not_i@type not_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p0@type@2 p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] 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-> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal6).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em or_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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-> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x3", + "=> (and false (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a and_i", + "=> false.", + "a x3", + "=> (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x3", + "=> (and (and false (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a x2", + "=> 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"a x", + "=> (iff (iff false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1473, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type iff_er).", + "c x", + "=> (x iff_i@type and_el@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1998, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c x", + "=> (x goal p2@type@2 iff_er).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e or_ir@type x1 or_ir).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P 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false]]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('A : prop) -> (not 'A) -> 'A -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('A : prop) -> (not 'A) -> 'A -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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-> 'P -> 'Q -> (and 'P 'Q)]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> false]; [(not [('A : prop) -> (not 'A) -> 'A -> false]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 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-> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [false -> ('P : prop) -> 'P]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a x1", + "=> (iff (not (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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-> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em false).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [false -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not false) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1477, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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-> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5986, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 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prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x0", + "=> false.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10968, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x) -> x -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "c x0", + "=> (x0 not_e@type goal not_e not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c em", + "=> (em p2@type@2).", + "c x1", + "=> (x1 iff_i@type or_ir@type iff_i or_ir).", + "c and_el", + "=> (and_el not_e@type goal p3).", + "a or_e", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso x1).", + "c x1", + "=> (x1 exfalso@type not_i@type exfalso not_i).", + "c x0", + "=> (x0 and_i@type and_er@type x1 and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "c x1", + "=> (x1 or_ir@type p3@type or_ir p3).", + "a exfalso", + "=> false.", + "a p4", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "c x0", + "=> (x0 goal and_el@type not_e and_el).", + "c x1", + "=> (x1 p2@type p6@type p2 p6).", + "c x1", + "=> (x1 p13@type p11@type p13 p11).", + "c x0", + "=> (x0 and_er@type p2@type and_er p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3282, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a 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(not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]]].", + "c x", + "=> (x p2@type p3@type p2).", + "c em", + "=> (em goal13).", + "c x", + "=> (x p2@type goal6 p2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": true, + "outcome": "solved", + "depth_used": 5, + "evals_used": 27, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> ." + ] + } + ], + "problem": "extrinsic_L0_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 24004, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 895, + "actions": [ + "c em", + "=> (em false).", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]; [(not false) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]].", + "c em", + "=> (em goal0).", + "a or_e", + "=> 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(and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not false))]) false).", + "a exfalso", + "=> false.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a x1", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 410, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1423, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x goal not_e@type iff_i).", + "c x", + "=> (x iff_i@type and_el@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_e@type or_e@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7442, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p0@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c x0", + "=> (x0 not_e@type goal19 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])])].", + "c x0", + "=> (x0 or_e@type and_i@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [false -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not false) -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 8517, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]].", + "c x0", + "=> (x0 not_e@type not_e@type x2 not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c x0", + "=> (x0 p0@type goal p0 iff_i).", + "c x1", + "=> (x1 exfalso@type or_il@type exfalso or_il).", + "c and_el", + "=> (and_el p0@type iff_i@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p5@type p4 p5).", + "c x1", + "=> (x1 not_e@type p9@type x2 p9).", + "c x0", + "=> (x0 and_i@type and_er@type and_i and_er).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]]]].", + "c x1", + "=> (x1 or_ir@type or_il@type or_ir or_il).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x0", + "=> (x0 em@type p5@type em p5).", + "c x1", + "=> (x1 p3@type p1@type p3 p1).", + "c x1", + "=> (x1 p14@type and_i@type p14 x0)." + ] + } + ], + "problem": "extrinsic_L0_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 23631, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + 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-> ['Q -> 'P]] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c x", + "=> (x not_i@type p@type not_i).", + "a exfalso", + "=> false.", + "c x", + "=> (x and_el@type or_e@type and_el).", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "c x", + "=> (x p@type goal2 p).", + "a x0", + "=> false.", + "a x0", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 624, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not 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prop) -> (not 'P) -> 'P -> false])) -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [false -> ('P : prop) -> 'P]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [false -> ('P : prop) -> 'P]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [false -> ('P : prop) -> 'P]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x0", + "=> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]].", + "a x0", + "=> (and [('A : prop) -> (or 'A (not 'A))] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]).", + "c em", + "=> (em goal20).", + "a x0", + "=> (and (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]])) (and [('A : prop) -> (or 'A (not 'A))] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [false -> ('P : prop) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 418, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", 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prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em", + "=> (em p4@type@2).", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7923, + "actions": [ + "c em", + "=> (em or_ir@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[x -> false] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "c x1", + "=> (x1 iff_er@type p0@type p0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c x0", + "=> (x0 exfalso@type not_i@type not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "c x1", + "=> (x1 p@type em@type em).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]].", + "intro.", + "c x1", + "=> (x1 goal3 p3@type p3).", + "c x1", + "=> (x1 p0@type@2 or_ir@type or_ir).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 or_ir@type exfalso@type x2).", + "c x0", + "=> (x0 goal6 p1@type p1).", + "a not_e", + "=> (not (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "c x1", + "=> (x1 p6@type or_ir@type or_ir).", + "a exfalso", + "=> false.", + "a x2", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x1", + "=> (x1 not_e@type or_ir@type x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2825, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ['A -> false] -> (not 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ['A -> false] -> (not 'A)]].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ['A -> false] -> (not 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ['A -> false] -> (not 'A)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "c x", + "=> (x goal iff_el@type not_i iff_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x iff_er@type goal x0 not_i).", + "c x", + "=> (x goal p2@type not_i p2).", + "c em", + "=> (em goal6).", + "c x", + "=> (x or_il@type and_el@type or_il and_el).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el goal p6@type p4).", + "intro.", + "intro.", + "c and_er", + "=> (and_er or_il@type and_el@type p6).", + "c and_er", + "=> (and_er goal p1@type p4).", + "c and_el", + "=> (and_el goal p6@type p4).", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a p8", + "=> (and (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a p8", + "=> (and (and (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> (and (and (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false)]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> (and (and (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false)].", + "c and_er", + "=> (and_er goal iff_el@type p4).", + "c and_el", + "=> (and_el goal p7@type@2 p2).", + "c em", + "=> (em p5@type@2).", + "a x0", + "=> (iff (and (and (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) false) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 351, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1038, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[false -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [false -> false]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[false -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[false -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[false -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[false -> false] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x not_i@type em@type not_i em).", + "a or_e", + "=> [[false -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [false -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em not_i@type).", + "c and_el", + "=> (and_el goal em@type p8).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 46, + "evals_used": 5748, + "actions": [ + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('A : prop) -> ['A -> false] -> (not 'A)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [('A : prop) -> ['A -> false] -> (not 'A)]].", + "intro.", + "c em", + "=> (em or_il@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] 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-> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)])]]]]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)])]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)])].", + "a x0", + "=> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 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-> (not 'A)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (iff (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a x1", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('A : prop) -> ['A -> false] -> (not 'A)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x" + ] + } + ], + "problem": "extrinsic_L0_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 8, + "evals_used": 19810, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 230, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal1).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(not [('P : prop) -> 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"depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + 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prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('A : prop) -> 'A -> (not (not 'A))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('A : prop) -> 'A -> (not (not 'A))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_er@type x1 iff_er).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1392, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or x (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> x.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4272, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> (not (not x))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('A : prop) -> 'A -> (not (not 'A))]); [('A : prop) -> 'A -> (not (not 'A))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('A : prop) -> 'A -> (not (not 'A))])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> 'A -> (not (not 'A))])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [false -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [false -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 556, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> 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-> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]]].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]] -> false]]]].", + "c em", + "=> (em p5@type@2).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 882, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", 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and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c and_er", + "=> (and_er em@type iff_i@type p4).", + "c x2", + "=> (x2 p@type and_i@type p x).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p5@type and_el@type p5 and_el).", + "a p8", + "=> (and [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] (not [false -> ('P : prop) -> 'P])).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1780, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em 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(not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not false) (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not false) (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]).", + "c em", + "=> (em goal18).", + "a x0", + "=> (and (or [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not false) (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]] (not [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not false) (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]])) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (not false) (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 407, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 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false]) -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not 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-> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (not 'P) -> 'P -> false])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> 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-> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 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+ "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c x2", + "=> (x2 and_er@type and_i@type and_er x2).", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])].", + "a x1", + "=> (iff (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type@2).", + "a iff_i", + "=> [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> [('P : prop) -> (or 'P (not 'P))]]; [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])].", + "a x1", + "=> (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]))].", + "c and_el", + "=> (and_el and_er@type and_i@type p2).", + "intro.", + "c and_er", + "=> (and_er and_er@type and_i@type p2).", + "c p6", + "=> (p6 and_er@type p1@type x3 p1).", + "a x3", + "=> (and (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]))).", + "a p5", + "=> (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> [('P : prop) -> (or 'P (not 'P))]] (and (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])))).", + "a x3", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> [('P : prop) -> 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x3", + "=> (and (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]])) (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) -> [('P : prop) -> (or 'P (not 'P))]] (and (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]) (iff [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]))))))).", + "a p5" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 377, + "actions": [ + "intro.", + "c em", + 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [x -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not x) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 521, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em not_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 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'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]]].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]]]; [(not [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] -> [[false -> ('P : prop) -> 'P] -> false]]]].", + "intro.", + "c em", + "=> (em goal15)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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-> false]; [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (or (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) false); [(and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "c em", + "=> (em or_il@type).", + "a or_il", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x1", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]]).", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (not x)); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] -> (and (and (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (or [('P : prop) -> 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]])].", + "c em", + "=> (em em@type).", + "a x1", + "=> (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] x)]]] (not x)) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a and_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", 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iff_i@type exfalso@type exfalso).", + "a x", + "=> (iff (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 p3@type@2 iff_i@type iff_i).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> (iff (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) -> (iff (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p@type).", + "a x", + "=> (iff (iff (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) -> false].", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4384, + "actions": [ + "intro.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('B : prop) -> ['B -> [x -> 'B]]]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type iff_el@type p0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('B : prop) -> ['B -> [x -> 'B]]]]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x0", + "=> (x0 exfalso@type goal1 exfalso).", + "c x0", + "=> (x0 em@type not_i@type em).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type p@type p0).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type p1@type or_ir).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]) -> false].", + "a or_e", + "=> [false -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> false]]; [(not false) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [false -> [false -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> false]]]; [(not false) -> [false -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "c em", + "=> (em p9@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 491, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p0@type@2).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L1_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 12, + "evals_used": 22346, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 163, + "actions": [ + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> false].", + "a exfalso", + "=> false.", + "a 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false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_il", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "c em", + "=> (em or_ir@type).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])) -> (not (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x2).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]).", + "a p8", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> false]; [(not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]) -> false].", + "a x", + "=> (or (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]) -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 1528, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L2_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 11844, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 278, + "actions": [ + "a 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (not false) [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])])).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal17).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false).", + "a x", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (and (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) false)).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 714, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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-> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 636, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (or false (not false))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not x2); x2.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not x2)]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not x2)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not x2)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not x2)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not x); x.", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 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prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x1", + "=> (or (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); [(not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a or_ir", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em iff_er@type).", + "c x0", + "=> (x0 goal7).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 425, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "c x0", + "=> (x0 not_e@type p1@type@2 p1).", + "a x", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "c x0" + ] + }, + { 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false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 475, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [('P : 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-> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [(or (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not (or (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (not (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))))) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]].", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[false -> ('P : prop) -> 'P] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 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prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 x3).", + "a x3", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [false -> ('P : prop) -> 'P]) (not [false -> ('P : prop) -> 'P])); [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [false -> ('P : prop) -> 'P]) -> (or (not [false -> ('P : prop) -> 'P]) (not [false -> ('P : prop) -> 'P]))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [false -> ('P : prop) -> 'P]) (not [false -> ('P : prop) -> 'P]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a 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-> [('C : prop) -> [x -> x0] -> [(and 'C x) -> (and 'C x0)]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em false).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not false) -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not false) -> false]]]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not false) -> false]]]]]].", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal13).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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+ "intro.", + "c em", + "=> (em and_er@type).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x1", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] false).", + "c em", + "=> (em or_e@type).", + "a x0", + "=> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]; false.", + "c x0", + "=> (x0 not_e@type iff_er@type not_e iff_er).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el not_e@type iff_er@type p5).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a x1", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 642, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em iff_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a x", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))).", + "a x", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))))) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "a x", + "=> (and (and false false) (and false false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and false false) (and false false))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and false false) (and false false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em goal10).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1482, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> 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"c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p4@type not_i@type p4 not_i).", + "c and_er", + "=> (and_er p4@type not_i@type p6).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c x0", + "=> (x0 not_i@type p1@type p7 p1).", + "c and_el", + "=> (and_el not_i@type p1@type p9).", + "a exfalso", + "=> false.", + "c and_er", + "=> (and_er not_i@type p1@type p9)." + ] + }, + { + "mode": "sample", 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goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type or_ir@type or_ir or_ir).", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "c x0", + "=> (x0 p0@type and_er@type p0 and_er).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c and_el", + "=> (and_el p0@type and_er@type p9).", + "c and_el", + "=> (and_el or_ir@type or_ir@type p5)." + ] + 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prop) -> (or 'P (not 'P))])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c not_e", + "=> (not_e and_i@type x2 and_i).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "intro.", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "c em", + "=> (em goal17).", + "c x", + "=> (x goal10 x2 x3).", + "c em", + "=> (em p2@type).", + "c x", + "=> (x and_i@type x3 and_i).", + "c x1", + "=> (x1 goal10 x2 x3).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 370, + "actions": [ + "a exfalso", + "=> 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('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or (or [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])) (not (or [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] (not [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B])))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1405, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a not_i", + "=> [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and x [false -> [false -> false]]).", + "a and_i", + "=> x; [false -> [false -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "c x0", + "=> (x0 not_e@type and_er@type x2 and_er).", + "c and_el", + "=> (and_el not_e@type and_er@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "c x1", + "=> (x1 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(and 'P 'Q) -> 'Q] -> false] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> ('P : prop) -> 'P])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c em", + "=> (em em@type).", + "a or_ir", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false].", + "c em", + "=> (em goal10).", + "a or_il", + "=> .", + "intro.", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('A : prop) -> (iff (or 'A 'A) 'A)]))); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('A : prop) -> (iff (or 'A 'A) 'A)])) -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('A : prop) -> (iff (or 'A 'A) 'A)])))]; [(not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> (iff (or 'A 'A) 'A)]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('A : prop) -> (iff (or 'A 'A) 'A)] [('A : prop) -> (iff (or 'A 'A) 'A)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [false -> ('P : prop) -> 'P]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "c iff_el", + "=> (iff_el p0@type@1 em@type p0).", + "c p3", + "=> (p3 exfalso).", + "a exfalso", + "=> false.", + "c p6", + "=> (p6 p10).", + "c em", + "=> (em goal0@1).", + "a p11", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c p3", + "=> (p3 p11).", + "a p11", + "=> false.", + "c x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 349, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : 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(em goal12).", + "intro.", + "a or_e", + "=> [x -> false]; [x -> false].", + "a x1", + "=> (iff false x).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "c em", + "=> (em goal0).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 537, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "intro.", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 goal12).", + "c em", + "=> (em x).", + "c x0", + "=> (x0 p5@type).", + "c iff_el", + "=> (iff_el p6@type@1 p5@type p6).", + "c x0", + "=> (x0 p@type@2).", + "c x0", + "=> (x0 p2@type).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p4@type@1 goal12 p4).", + "a exfalso", + "=> false.", + "c iff_el", + "=> (iff_el p8@type@1 p@type@2 p8).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "c iff_er", + "=> (iff_er p9@type@1 p2@type p9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 499, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or x x) -> x]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", 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(not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]]))).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]] -> (not (or [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]] (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]])))]; [(not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]]) -> (not (or [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]] (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(or x x) -> x]]])))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c x2", + "=> (x2 p@type or_ir@type p or_ir).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x2).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and (and (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a p8", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and (and (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 385, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + 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-> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", 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-> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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"intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not false) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [false -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not false) -> [false -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 562, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "c x0", + "=> (x0 goal10).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 495, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "c em", + "=> (em em@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]].", + "c em", + "=> (em p0@type@2).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]])) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]].", + "intro.", + "c x0", + "=> (x0 and_er).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]]]]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> (or 'P (not 'P))] (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))))]).", + "c x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) -> false].", + "a or_e", + "=> [false -> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false]]; [(not false) -> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false]].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> [false -> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false]]]; [(not (not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))])) -> [false -> [(not [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]) -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not false) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not false) -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not false) -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not false) -> false]]].", + "c em", + "=> (em p9@type@2).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3107, + "actions": [ + "c em", + "=> (em 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(iff 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c em", + "=> (em p@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 628, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 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p1@type@2).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]] -> false].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]] -> false]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff x 'B) -> (iff 'B x)]] -> false]].", + "intro.", + "c em", + "=> (em goal8).", + "c em" + ] + }, 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: prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] (not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type 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"actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "a x0", + "=> (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x1", + "=> (x1 em).", + "intro.", + "a x2", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_ir", + "=> .", + "a x0", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "c p3" + ] + } + ], + "problem": "extrinsic_L2_12" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 8, + "evals_used": 21460, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 278, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> 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false)] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)] [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 354, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2164, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> false]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> 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em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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+ "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : 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false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (not false); false.", + "c em", + "=> (em goal5).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em x0).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not false)); (not false).", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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"=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 360, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + 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[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 8670, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(and x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(and x 'B) -> 'C]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(and x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(and x 'B) -> 'C]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er)." + ] + } + ], + "problem": "extrinsic_L3_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 33703, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + 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prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0); x0.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x0)]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not x0)].", + "c x1", + "=> (x1 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]].", + "a x2", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) x0); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [x0 -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x2", + "=> (or [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) x0)]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) x0)].", + "c x1", + "=> (x1 p1@type p1@type p1).", + "a x1", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 352, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + 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prop) -> (or 'P (not 'P))] false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 679, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a 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prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x1", + "=> (x1 not_e@type or_il@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4373, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P 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[('P : prop) -> (or 'P (not 'P))]))))].", + "c x2", + "=> (x2 p@type or_ir@type p or_ir).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er and_i).", + "c x2", + "=> (x2 p5@type or_il@type p5 or_il).", + "a x1", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))))]).", + "a p8", + "=> (and false (and (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a 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-> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]) -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : 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: prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x0", + "=> (x0 p@type iff_i@type iff_i).", + "c x0", + "=> (x0 p@type iff_el@type iff_el).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))] (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 iff_i@type or_e@type or_e)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 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'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> 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and_i", + "=> (not false); [false -> [false -> false]].", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c 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(x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 387, + "actions": [ + "intro.", + "intro.", + "intro.", + "c em", + "=> (em x0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x3", + "=> (iff [false -> ('P : prop) -> 'P] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]; 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-> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]]].", + "a x3", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]])].", + "a x3", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]])).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p3@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> (not 'P) -> 'P -> false] [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [false -> ('P : prop) -> 'P] false)]]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 42, + "evals_used": 3268, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 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or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> false]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]]] -> false]]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]); [[('P : prop) -> (or 'P (not 'P))] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [[false -> ('P : prop) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])].", + "a x" + ] + } + ], + "problem": "extrinsic_L3_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 21839, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em 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prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]]]]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) 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x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p13@type and_er p13).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p)." + ] + } + ], + "problem": "extrinsic_L3_5" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 23822, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 278, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a 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false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : 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-> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]])].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 536, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + 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'P]])))) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 449, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "a or_il", + "=> .", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [false -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 610, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a x1", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a and_i", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]); (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]).", + "a and_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a x1", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]])).", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "a exfalso", + "=> false.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] false).", + "a x1", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] false)).", + "a or_e" + ] + }, + { + "mode": "sample", 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c x0", + "=> (x0 iff_i@type or_e@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 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-> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "a x0", + "=> (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "intro.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 13641, + "actions": [ + "a exfalso", + "=> 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])].", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal6).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]))))) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])); [(or (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> 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(or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a x", + "=> (or (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]); [(or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) -> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])] -> (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p0@type).", + "a or_il", + "=> .", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]))]; [(not [false -> ('P : prop) -> 'P]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or (or (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> (or 'P (not 'P))] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]))].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] 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not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]); [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x0", + "=> false.", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2778, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(or false (not false)) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 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-> (not (or 'A 'B))]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p4@type or_ir@type x0).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]].", + "c x0", + "=> (x0 em@type p7@type p7).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> 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: prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])) (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])); [(or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])) -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])) (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])) (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]].", + "intro.", + "a or_e", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not 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'R] -> 'R]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false)]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false)].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> .", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c em", + "=> (em p@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or (not [false -> ('P : prop) -> 'P]) (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false)); [(not [false -> ('P : prop) -> 'P]) -> false]; [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [false -> ('P : prop) -> 'P]) (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false))]; [[('P : prop) -> (or 'P (not 'P))] -> (or (not [false -> ('P : prop) -> 'P]) (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false))].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or (not 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false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x", + "=> (x not_e@type p6@type@2 p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 508, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]].", + "a or_e", + 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-> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a x1", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]).", + "a and_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a x1", + "=> (and [('P : 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-> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [false -> ('P : prop) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a 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['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] [('P : prop) -> ['P -> false] -> (not 'P)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 529, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p@type@2).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4522, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]))); (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])).", + "c and_er", + "=> (and_er em@type iff_i@type p4).", + "c x2", + "=> (x2 p@type and_i@type p x).", + "c x2", + "=> (x2 iff_el@type em@type iff_el em).", + "c x2", + "=> (x2 p5@type and_el@type p5 and_el).", + "a p8", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] (not (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])))).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false].", + "a x", + "=> (and [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [false -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1459, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]] -> [false -> [false -> false]]].", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + } + ], + "problem": "extrinsic_L3_13" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 13624, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 481, + "actions": [ + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> (iff (not 'A) ['A -> false])]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('A : prop) -> (iff (not 'A) ['A -> false])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em exfalso@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1207, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "intro.", + "c x", + "=> (x p4@type@2 iff_el@type iff_el).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "intro.", + "a not_e", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> 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false]].", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal9).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not x0)); (not x0).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a or_e", + "=> [[(not x0) -> [x0 -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]; [(not [(not x0) -> [x0 -> false]]) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not x0) -> [x0 -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[(not x0) -> [x0 -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not x0) -> [x0 -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[(not x0) -> [x0 -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x0) -> [x0 -> false]]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x0) -> [x0 -> false]]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c x3", + "=> (x3 goal9 p@type p).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 419, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 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-> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2058, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + 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['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 314, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> 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+ "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type goal3 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]] -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]]].", + "a x2", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]]]].", + "a x2", + "=> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]); [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])] -> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a x2", + "=> (or [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])])].", + "c x1", + "=> (x1 p1@type goal10 p1).", + "a x1", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2955, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) -> false].", + "c x", + "=> (x not_i@type iff_er@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 not_i@type p5).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]) -> false].", + "c x0", + "=> (x0 p@type@2 or_ir@type).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2306, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 and_i@type iff_i@type and_i).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))); (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]].", + "c x0", + "=> (x0 not_i@type goal not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false]]].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em goal10).", + "c x0", + "=> (x0 iff_el@type goal1 iff_el).", + "intro.", + "intro.", + "c not_e", + "=> (not_e p0@type x3 p0).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : 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'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not false) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 30, + "evals_used": 2479, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or x 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-> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 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-> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "a x0", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a x0", + "=> (and (and [('P : prop) -> (not 'P) -> 'P -> false] false) (and [('P : prop) -> (not 'P) -> 'P -> false] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (and [('P : prop) -> (not 'P) -> 'P -> false] 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-> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false]); [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false].", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x1", + "=> (x1 iff_i@type goal).", + "c iff_el", + "=> (iff_el p1@type@1 iff_i@type p1).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p0@type@2).", + "c x1", + "=> (x1 p1@type@1 p1@type@1@2).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P 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-> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1624, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A 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'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 618, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : 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-> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c em", + "=> (em goal4).", + "intro.", + "intro.", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a x0", + "=> (and (or [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (or [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (or [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)])).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)])) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 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false))))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]]).", + "c em", + "=> (em goal23).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 442, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> 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[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 554, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not (not (not 'A))) -> (not 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (not (not (not 'A))) -> (not 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em goal4).", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a x", + "=> (not [x0 -> false]); [x0 -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a x3", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p2@type@2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + 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p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1983, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]); [('A : prop) -> (not (not (not 'A))) -> (not 'A)].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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'Q)])) -> false]); [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal16).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1461, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P 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prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])]] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])]] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]].", + "a x0", + "=> (iff [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])]] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal18).", + "a x", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])]] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]]) (iff [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)])]] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 423, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a and_i", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em em@type).", + "intro.", + "a x0", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) false).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) false)).", + "c em", + "=> (em goal17).", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) false).", + "a or_e", + "=> [(and [('P : prop) -> ['P -> false] -> (not 'P)] false) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) false)]; [(not (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) -> (and (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false) false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 452, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c not_e", + "=> (not_e not_i@type x0 not_i).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> false]].", + "intro.", + "a x0", + "=> (iff false false).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 362, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e not_e@type x1 not_e).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_il@type).", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "c em", + "=> (em goal3).", + "intro.", + "c not_e", + "=> (not_e exfalso@type x0 exfalso).", + "intro.", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em not_i@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]) -> false].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]) -> false]]; [(and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]) -> [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]))]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]))].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))]))))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]))]; [(or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])) (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (or 'P (not 'P))])))) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x p@type@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1409, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + 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(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]); [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or false [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]); [false -> (or [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false])]; [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> (or [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff false false)); (iff false false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (iff false false))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (iff false false))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (iff false false))).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (iff false false)))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not (iff false false)))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 4229, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]])] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0)." + ] + } + ], + "problem": "extrinsic_L3_18" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 11, + "evals_used": 17919, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 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false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> 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+ "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", 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['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 621, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or (and x 'B) (and x 'C)) -> (and x (or 'B 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x 'B) 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[(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal9).", + "c 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-> false]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))) (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [false -> ('P : prop) -> 'P] false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> 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prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e em@type x1 em).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; 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'P) -> 'P -> false]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a and_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7061, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff 'A (not 'A)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff 'A (not 'A)) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1459, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not false) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not false) -> [false -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (not false) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [(not false) -> [false -> [false -> false]]]; [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [false -> [false -> false]]].", + "a or_il", + "=> (not false).", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12557, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(iff x (not x)) -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(iff x (not x)) -> false]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c iff_er", + "=> (iff_er x x2@type@2 x2).", + "c iff_el", + "=> (iff_el x x2@type@2 x2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 iff_i@type p1@type iff_i p1).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso or_il).", + "c p9", + "=> (p9 exfalso@type not_e@type exfalso not_e).", + "c x1", + "=> (x1 and_i@type and_i@type p9 and_i).", + "c x0", + "=> (x0 exfalso@type not_e@type exfalso not_e).", + "a exfalso", + "=> false.", + "c p9", + "=> (p9 or_il@type not_e@type or_il not_e).", + "c em", + "=> (em x2@type@2).", + "c x1", + "=> (x1 iff_er@type p12@type iff_er p14).", + "c x1", + "=> (x1 p0@type exfalso@type p0 exfalso).", + "c p9", + "=> (p9 p7@type p11@type p7 p11).", + "c p9", + "=> (p9 p17@type p15@type p17 p15).", + "c x1", + "=> (x1 and_el@type p5@type and_el p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2214, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not 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'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "intro.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a x0", + "=> (and (not (or x (not x))) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal0@1@1@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 634, + "actions": [ + "intro.", + "c em", + "=> (em x).", + "a not_i", + "=> [(not (or x (not x))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal11).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not (not (or x (not x)))) (not (not (not (or x (not x))))))).", + "a not_i", + "=> [(or (not (not (or x (not x)))) (not (not (not (or x (not x)))))) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [(or (not (not (or x (not x)))) (not (not (not (or x (not x)))))) -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) -> [(or (not (not (or x (not x)))) (not (not (not (or x (not x)))))) -> false]].", + "intro.", + "c x1", + "=> (x1 and_i).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 590, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em goal0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (and false (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a and_i", + "=> false; (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a x1", + "=> (and (not [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e" + ] + }, + { + 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-> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a p4", + "=> (or x0 (not (or x0 (not x0)))); [x0 -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [(not (or x0 (not x0))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 exfalso@type).", + "a p4", + "=> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [false -> (or x0 (not (or x0 (not x0))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or x0 (not (or x0 (not x0))))].", + "c em", + "=> (em p6@type).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or x0 (not (or x0 (not x0))))); [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(or x0 (not (or x0 (not x0)))) -> (or false (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a p4", + "=> (or (not (or (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))))) (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))); [(not (or (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))))) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or x0 (not (or x0 (not x0)))))]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or x0 (not (or x0 (not x0)))))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a x", + "=> (and [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a and_i", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [('P : prop) -> (or 'P (not 'P))]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> 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[false -> false] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> false] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> false] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) 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prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not false))].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P 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['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 265, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 637, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not 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-> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]))].", + "intro.", + "c em", + "=> (em not_i@type).", + "a x0", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [false -> ('P : prop) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[false -> ('P : prop) -> 'P] -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> 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['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "c x1", + "=> (x1 or_e).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2109, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (or [false -> 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'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c p8", + "=> (p8 goal p0@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6240, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "intro.", + "c x1", + "=> (x1 iff_er@type iff_er@type iff_er iff_er).", + "c and_er", + "=> (and_er iff_er@type iff_er@type p1).", + "c x1", + "=> (x1 iff_el@type exfalso@type iff_el exfalso).", + "c x1", + "=> (x1 iff_er@type p3@type iff_er p3).", + "c em", + "=> (em p1@type).", + "c x1", + "=> (x1 or_il@type and_i@type or_il x1).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c and_el", + "=> (and_el or_il@type and_i@type p6).", + "intro.", + "intro.", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c and_er", + "=> (and_er or_il@type and_i@type p6).", + "c and_el", + "=> (and_el iff_el@type exfalso@type p3).", + "a p10", + "=> (iff (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "c p9", + "=> (p9 iff_el@type and_i@type p10 x4).", + "c p9", + "=> (p9 p3@type p7@type p3 p7).", + "c p8", + "=> (p8 p6@type p@type p6).", + "c x1", + "=> (x1 not_e@type or_il@type not_e or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 711, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + 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prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7372, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> (or 'P (not 'P))]); [false -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]])); [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> (or 'P (not 'P))])]]]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [[('P 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-> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]]) -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_el@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em 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false]].", + "intro.", + "a x0", + "=> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]]] -> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [x -> (not (not x))]]]]) -> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "c em", + "=> (em goal0@2@1).", + "c x3", + "=> (x3 p5@type@2).", + "intro.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (iff false (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "c x3", + "=> (x3 p7@type@2).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1567, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (iff 'A (not (not 'A)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (iff 'A (not (not 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-> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "c x3", + "=> (x3 goal9 not_e@type x).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a x", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> (or 'P (not 'P))] -> false] [('P : prop) -> (or 'P (not 'P))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", 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[false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x", + "=> (or false false); [false -> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [false -> (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_ir", + "=> false.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) -> (or [false -> ('P : prop) -> 'P] (or false false))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [false -> ('P : prop) -> 'P] (or false false))].", + "a x", + "=> (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) -> (or (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> .", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))))); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]]; [(or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) (not (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [[false -> ('P : prop) -> 'P] 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'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x2", + "=> (x2 p@type or_ir@type p or_ir).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]).", + "a p8", + "=> (and (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])) (and (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q 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'A) -> 'B] -> 'B]) -> (and [[false -> ('P : prop) -> 'P] -> false] (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 p@type@2 and_er@type and_er).", + "c x0", + "=> (x0 p@type@2 or_ir@type or_ir).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x0", + "=> (x0 exfalso@type iff_i@type iff_i)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) 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-> false] -> (not 'P)] false)])].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)])]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (or [('P : prop) -> ('Q : 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 625, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not x) -> (not 'B)] -> ['B -> x]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [false -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not false) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [false -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> 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+ "=> (x1 iff_i@type iff_el@type iff_i iff_el).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 477, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em iff_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (iff false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p4@type).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not false) (not (not false)))).", + "a not_i", + "=> [(or (not false) (not (not false))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal11).", + "a x", + "=> (iff false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [(not false) -> (iff false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not (not false)) -> (iff false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 395, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))); (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4691, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 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false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [false -> false]]; [(not [false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]) -> [false -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]] -> [false -> false]]]; [(not [false -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (and 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'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]].", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [[(not 'B) -> (not x)] -> [x -> 'B]]]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x0", + "=> (x0 not_e).", + "c p2", + "=> (p2 not_e@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not x) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em goal2).", + "c em", + "=> (em and_el@type).", + "intro.", + "c p2", + "=> (p2 goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c p2", + "=> (p2 goal2).", + "c em" + ] + } + ], + "problem": "extrinsic_L4_5" + }, + { + "solved": false, + "greedy_solved": false, + 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p7@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))); (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] 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[(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))); (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])))); (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]) -> (not (not (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 443, 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]).", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [x -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not x) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 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[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 iff_el@type iff_el@type iff_el).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 p@type and_er@type and_er).", + "c x0", + "=> (x0 p@type or_il@type or_il).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false]))); [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(or [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false])]] -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false])))].", + "c x0", + "=> (x0 iff_i@type and_el@type and_el)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1463, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 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false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false] -> false]; [(not [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 533, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]; [(not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [[false -> ('P : prop) -> 'P] -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]]]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> [[false -> ('P : prop) -> 'P] -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) -> false]]].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] -> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> [[false -> ('P : prop) -> 'P] -> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 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: prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + 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'Q -> (and 'P 'Q)])].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9118, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c x0", + "=> (x0 em@type or_e@type em or_e).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2602, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_il@type or_il).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type or_ir@type x0).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false)]].", + "intro.", + "intro.", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2662, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not (and x x0)) -> (or (not x) (not x0))]].", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (and x x0)) -> (or (not x) (not x0))]] -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em x).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "c em", + "=> (em goal6).", + "intro.", + "intro.", + "intro.", 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9124, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]].", + "c x0", + "=> (x0 not_e@type or_il@type not_e or_il).", + "c and_el", + "=> (and_el not_e@type or_il@type p3).", + "c x0", + "=> (x0 p0@type p2@type p0 p2).", + "c x1", + "=> (x1 not_e@type p2@type p4 p2).", + "c and_el", + "=> (and_el p0@type p2@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type p1@type not_e p1).", + "c x1", + "=> (x1 not_e@type p5@type not_e p5).", + "c x0", + "=> (x0 and_i@type and_el@type x1 and_el).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff [x -> 'B] (or (not x) 'B))]]]]].", + "c x1", + "=> (x1 or_il@type p11@type or_il p11).", + "a exfalso", + "=> false.", + "a x2", + "=> (not false); false.", + "c x0", + "=> (x0 em@type or_ir@type em or_ir).", + "c x1", + "=> (x1 p3@type p13@type p3 p13).", + "c x1", + "=> (x1 p14@type and_el@type p14 and_el).", + "c x0", + "=> (x0 and_er@type or_il@type and_er or_il)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 556, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P 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(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))].", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))])].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 34, + "evals_used": 882, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> (not 'P) -> 'P -> false])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a p4", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 472, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal8).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + 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"=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> (and [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]) -> (and [(or [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]])) -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", 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exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false] [('P : prop) -> (or 'P (not 'P))]); [[[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 266, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : 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(iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]].", + "intro.", + "c em", + "=> (em false).", + "intro.", + "a x2", + "=> (or [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (or x [x -> 'B])]]]]); [[(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (or x [x -> 'B])]]]] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em p2@type@2).", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : 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prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c x2", + "=> (x2 and_er@type and_i@type and_er x2).", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c em", + "=> (em p1@type@2).", + "a iff_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> (or 'P (not 'P))]].", + "a x1", + "=> (iff [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (iff [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (iff [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "c and_el", + "=> (and_el and_er@type and_i@type p2).", + "intro.", + "c and_er" + ] + } + ], + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + 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-> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "c x", + "=> (x and_el@type em@type and_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : 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+ "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)); (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) false).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)).", + "c em", + "=> (em goal14).", + "a and_i", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 404, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [x -> (not x)]) -> x]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [x -> (not x)]) -> x]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "a not_i", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false].", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c not_e", + "=> (not_e and_i@type x0 and_i).", + "c em", + "=> (em em@type).", + "c em", + "=> (em p2@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em goal3)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3962, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_il", + "=> .", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]]; [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> false]); [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[false -> ('P : prop) -> 'P] -> false])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]].", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]] -> false].", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]] -> false]].", + "c and_el", + "=> (and_el em@type em@type p2).", + "c p5", + "=> (p5 not_e@type).", + "a p4", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or (not [false -> ('P : prop) -> 'P]) (not [[false -> ('P : prop) -> 'P] -> false])); [(not [false -> ('P : prop) -> 'P]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a p4", + "=> (or (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> (or (not [false -> ('P : prop) -> 'P]) (not [[false -> ('P : prop) -> 'P] -> false]))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (not [false -> ('P : prop) -> 'P]) (not [[false -> ('P : prop) -> 'P] -> false]))].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 413, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> (not false)]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not false)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a 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'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]]); [[('P : prop) -> (or 'P (not 'P))] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> [(not 'A) -> 'A] -> 'A]] -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 668, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x) -> x] -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x) -> x] -> x]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[(not x) -> x] -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(not x) -> x] -> x]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x1", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]])); [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x1", + "=> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> (or 'P (not 'P))] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> false]]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_ir", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]].", + "intro.", + "a x1", + "=> (or [('P : prop) -> (or 'P (not 'P))] [x -> false]); [[('P : prop) -> (or 'P (not 'P))] -> [x -> false]]; [[x -> false] -> [x -> false]]." + ] + } + ], + "problem": "extrinsic_L4_12" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 11, + "evals_used": 49962, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 163, + "actions": [ + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]; [(not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 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prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "c x", + "=> (x p0@type p@type p0 p).", + "c and_er", + "=> (and_er p0@type p@type p5).", + "c and_el", + "=> (and_el p0@type p@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em not_e@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 28778, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [('A : prop) -> 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or_il@type p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4649, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q 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(or 'P (not 'P))]))))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))])) (or (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]))) (not (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]))))))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])); [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [false -> ('P : prop) -> 'P] (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(or [false -> ('P : prop) -> 'P] (or [false -> ('P : prop) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])) -> false].", + "c 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (or (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]))) (not (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))])))))); [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) -> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]))) (not (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) (not (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]))))) -> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3372, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]).", + "a p8", + "=> (and (not [('P : prop) -> ('Q : prop) -> 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 655, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and (not x) 'B)) (or x 'B))]].", + "c em", + "=> (em 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prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + 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(not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2155, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + 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x2) -> (and x (or (not x) x2))]].", + "a exfalso", + "=> .", + "intro.", + "intro.", + "a exfalso", + "=> .", + "c em", + "=> (em iff_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and x (or (not x) 'B)) (and x 'B))]]].", + "c not_e", + "=> (not_e false x1 x0).", + "c not_e", + "=> (not_e false x1 p3).", + "intro.", + "a exfalso", + "=> .", + "c not_e", + "=> (not_e false x1 x0).", + "c em", + "=> (em or_ir@type).", + "c not_e", + "=> (not_e false x1 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exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7302, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> 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: prop) -> (and 'P 'Q) -> 'Q] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; 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'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [false -> [false -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 647, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a iff_i", + "=> [(or (and x x2) (and x (not 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2786, + "actions": [ + "a 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-> false] false).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false)].", + "c em", + "=> (em goal24)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> 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false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2282, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em false).", + "a x0", + "=> (not (not false)); (not false).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not (not false))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not (not false))].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type iff_el@type p4).", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> false] -> [x -> false]]; [(not [false -> false]) -> [x -> false]].", + "c x1", + "=> (x1 not_e@type and_er@type x0).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7023, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> false].", + "intro.", + "a x", + "=> (not x0); x0.", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [x0 -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c x1", + "=> (x1 iff_i@type p@type@2).", + "c iff_el", + "=> (iff_el p1@type@1 iff_i@type p1).", + "c em", + "=> (em p1@type@1@1).", + "c em", + "=> (em goal7).", + "c x1", + "=> (x1 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: prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "c x2", + "=> (x2 p0@type goal p0 x1).", + "c x2", + "=> (x2 em@type iff_i@type em iff_i).", + "c x2", + "=> (x2 p4@type iff_i@type p4 iff_i).", + "c x1", + "=> (x1 p6@type p1@type).", + "c iff_er", + "=> (iff_er p5@type@1 p1@type@1 p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])); (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]).", + "a not_i", + "=> [(not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])) -> false]; [(not (not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]))) -> false].", + "a x", + "=> (and [(not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])) -> false] (or [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]))).", + "a and_i", + "=> [(not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6489, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type p0@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1325, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or x [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> x.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 703, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(and (or x x2) (or x (not x2))) -> x]; [x -> (and (or x x2) (or x (not x2)))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or x (not x2))); (or x (not x2)).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em x).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal4@1@1).", + "c em", + "=> (em goal12).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em exfalso@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2483, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P 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-> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 644, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [('P : prop) 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-> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))))) (and (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))))))]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))) (and (and (or (not [('P : prop) -> ('Q : prop) -> (and 'P 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))) (and (and (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))))) (and (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7739, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : 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-> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]); [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('A : prop) -> ('B : prop) -> (iff (not (iff 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-> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "c not_e", + "=> (not_e or_ir@type x2 or_ir).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "intro.", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "intro.", + "c em", + "=> (em goal17).", + "c x", + "=> (x goal10 x2 x3).", + "c em", + "=> (em p2@type).", + "c x", + "=> (x or_ir@type x3 or_ir).", + "c x1", + "=> (x1 goal10 x2 x3).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false].", + "a x", + "=> (and [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", 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[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> 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"a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + 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(iff 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em p1@type@2).", + "a x", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "c em", + "=> (em and_el@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 689, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]); [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and [('P : prop) -> (or 'P (not 'P))] false)].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)])].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)])]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and [('P : prop) -> (or 'P (not 'P))] false)])]].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : 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'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]].", + "c em", + "=> (em iff_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "c em", + "=> (em p0@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3175, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [false -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a or_e", + "=> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not false) -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [false -> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not false) -> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c em", + "=> (em p@type).", + "intro.", + "a x0", + "=> (iff [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] false).", + "a iff_i", + "=> [[false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))] -> false]; [false -> [false -> (not (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type@2).", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 466, + "actions": [ + "c em", + "=> (em iff_i@type).", + "a 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-> 'Q -> (and 'P 'Q)] -> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))])) -> (not x0)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))])) -> (not x0)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))])) -> (not x0)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [('A : 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"c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]; [(not [[false -> ('P : prop) -> 'P] -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]].", + "c em", + "=> (em p6@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6472, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [false -> (or (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false])) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 366, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) 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['P -> 'Q]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x0", + "=> (or false [false -> ('P : prop) -> 'P]); [false -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (or false [false -> ('P : prop) -> 'P])]; [(not [false -> ('P : prop) -> 'P]) -> (or false [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em not_i@type).", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x1", + "=> false.", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 866, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> 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(em p4@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]])].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal0).", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))); (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 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-> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]] -> false]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [(or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))) -> (not [('P : prop) 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(x1 iff_i@type or_il@type).", + "c iff_el", + "=> (iff_el p1@type@1 p1@type@2 p1).", + "c em", + "=> (em p1@type@1@2).", + "c em", + "=> (em goal10).", + "c x1", + "=> (x1 p1@type@2 and_er@type).", + "a or_e", + "=> [(and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "c and_el", + "=> (and_el p1@type@1@2@1 or_il@type x2).", + "intro.", + "intro.", + "c not_e", + "=> (not_e iff_i@type p6 iff_i).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c and_er", + "=> (and_er p1@type@1@2@1 or_il@type x2).", + "c p8", + "=> (p8 p0@type and_el@type p0).", + "c p8", + "=> (p8 iff_er@type p1@type@2@1 iff_er).", + "c p8", + "=> (p8 p3@type or_ir@type p3).", + "c x3", + "=> (x3 p5@type iff_er@type p5 iff_er).", + "c x", + "=> (x iff_i@type p6 iff_i)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 381, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 39753, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x p3@type@2 p3@type@2 not_e@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q 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('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]].", + "c em", + "=> (em goal1).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal2).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "intro.", + 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prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]).", + "c em", + "=> (em goal13).", + "a x", + "=> (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]).", + "a x", + "=> (and (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> 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prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> (and (and (and (and (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) (and false false)) (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e", + "=> [(and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and (and (and (and (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) (and false false)) (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (and (and (and (and (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) (and false false)) (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))].", + "a x", + "=> (and [(and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and (and (and (and (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) (and false false)) (and (and (and (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])) [('P : prop) -> (not 'P) -> 'P -> false]) (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)])).", + "c em", + "=> (em goal7).", + "a and_i", + "=> false; (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]).", + "a or_e", + "=> [(and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false]; [(not (and (and false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 489, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c not_e", + "=> (not_e not_e@type x not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]]]].", + "c em", + "=> (em p6@type@2).", + "a exfalso", + "=> .", + "c em", + "=> (em goal8)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em p@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 609, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)].", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em goal10).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [false -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [false -> false]].", + "intro.", + "c em", + "=> (em p5@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2057, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))); (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c p8", + "=> (p8 goal and_i@type and_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_il@type p5 or_il).", + "a x1", + "=> (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]).", + "a p8", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 415, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])).", + "a and_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a x", + "=> (and [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> (and [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> (and [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not false)]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 59, + "evals_used": 6287, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [false -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[false -> ('P : prop) -> 'P] -> false] (not [false -> ('P : prop) -> 'P])); [[[false -> ('P : prop) -> 'P] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or (not [[false -> ('P : prop) -> 'P] -> false]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]); [(not [[false -> ('P : prop) -> 'P] -> false]) -> (or [[false -> ('P : prop) -> 'P] -> false] (not [false -> ('P : prop) -> 'P]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]] -> (or [[false -> ('P : prop) -> 'P] -> false] (not [false -> ('P : prop) -> 'P]))].", + "c x0" + ] + } + ], + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 20349, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 938, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]; [(not false) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]; [(not [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]) -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]].", + "a or_e", + "=> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]]; [(not [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]) -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]].", + "a or_e", + "=> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]]]; [(not [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]) -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]]].", + "c em", + "=> (em goal).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em 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-> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C 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(not 'A) 'B)))]])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c em", + "=> (em p2@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 x).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 708, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", 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"a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2039, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; 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: prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e em@type x1 em).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1459, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not 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false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]] [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "c em", + "=> (em and_er@type).", + 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"=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er x).", + "c x2", + "=> (x2 p5@type or_ir@type p5 or_ir).", + "c p8", + "=> (p8 p5@type or_ir@type p11).", + "a p8", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 417, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not false)]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[false -> false] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 627, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (iff (iff x (iff 'B 'C)) (iff (iff x 'B) 'C))]]; [(not [('P : prop) -> 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or_e", + "=> [[[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> 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-> false] -> (not 'P)] false) false)))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false false).", + "c em", + "=> (em goal12).", + "a and_i", + "=> false; false.", + "a or_e", + "=> [(and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) false) -> false]; [(not (and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) false)) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) false) -> false]; [(not (and (and [('P : prop) -> ['P -> false] -> (not 'P)] false) false)) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 648, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> 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(iff 'P 'Q) -> ['P -> 'Q]])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a x0", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[false -> ('P : prop) -> 'P] -> (not (not [false -> ('P : prop) -> 'P]))]) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "a x", + "=> false.", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] false)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 425, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))); [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [(not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]] -> (or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))) (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 332, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 679, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or (and x (and 'B 'C)) (or (not x) (or (not 'B) (not 'C))))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or (and x (and 'B 'C)) (or (not x) (or (not 'B) 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or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x)]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x)]]); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x)]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('B : prop) -> ('C : prop) -> (or 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false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type or_ir).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", 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false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[false -> ('P : prop) -> 'P] -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..0a6f32a320632ee2dce70c2016143e72476cfa34 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,953 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[ ] - extrinsic_L0_3 (traces=17 evals=17591) +[ ] - extrinsic_L0_2 (traces=16 evals=29952) +[ ] - extrinsic_L0_1 (traces=6 evals=18636) +[ ] - extrinsic_L0_4 (traces=17 evals=30924) +[ ] - extrinsic_L0_6 (traces=14 evals=36828) +[ ] - extrinsic_L0_5 (traces=14 evals=25475) +[OK ] - extrinsic_L0_10 (traces=5 evals=6108) + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345408) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ['A -> false] -> (not 'A)] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (x [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] not_i (and_el [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (x [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] or_ir or_e)))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] (and [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) and value type (and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) did not unify. + +thread '' (1345408) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ['A -> false] -> (not 'A)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (x [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) not_i (x [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] not_i iff_el))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) and value type (and [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) did not unify. +[ ] - extrinsic_L0_8 (traces=17 evals=14039) +[ ] - extrinsic_L0_7 (traces=17 evals=25870) +[ ] - extrinsic_L0_12 (traces=17 evals=23631) +[ ] - extrinsic_L0_9 (traces=14 evals=38745) +[ ] - extrinsic_L0_11 (traces=13 evals=24004) +[ ] - extrinsic_L0_13 (traces=11 evals=25962) + +thread '' (1345409) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L1_2 (traces=17 evals=18315) +[ ] - extrinsic_L0_14 (traces=8 evals=19810) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_1 (traces=17 evals=29317) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_3 (traces=17 evals=25790) + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L1_4 (traces=17 evals=21498) + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_1 (traces=12 evals=22346) +[ ] - extrinsic_L2_2 (traces=17 evals=11844) +[ ] - extrinsic_L2_4 (traces=17 evals=27060) +[ ] - extrinsic_L2_3 (traces=11 evals=22727) +[ ] - extrinsic_L2_5 (traces=17 evals=24733) +[ ] - extrinsic_L2_6 (traces=17 evals=28288) +[ ] - extrinsic_L2_7 (traces=14 evals=18313) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_8 (traces=14 evals=31375) +[ ] - extrinsic_L2_9 (traces=8 evals=25698) +[ ] - extrinsic_L2_11 (traces=17 evals=27551) +[ ] - extrinsic_L2_10 (traces=17 evals=22026) + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_12 (traces=14 evals=18305) +[ ] - extrinsic_L2_13 (traces=8 evals=21460) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_1 (traces=17 evals=18925) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=13 evals=24915) +[ ] - extrinsic_L3_3 (traces=13 evals=33703) + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_4 (traces=15 evals=31406) + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=17 evals=23822) + +thread '' (1345409) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_5 (traces=13 evals=21839) + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=14 evals=25574) +[ ] - extrinsic_L3_8 (traces=15 evals=22364) +[ ] - extrinsic_L3_9 (traces=16 evals=27286) +[ ] - extrinsic_L3_10 (traces=8 evals=23984) +[ ] - extrinsic_L3_12 (traces=17 evals=25062) +[ ] - extrinsic_L3_11 (traces=14 evals=22879) +[ ] - extrinsic_L3_14 (traces=17 evals=13624) +[ ] - extrinsic_L3_16 (traces=17 evals=27026) +[ ] - extrinsic_L3_13 (traces=13 evals=30000) + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_15 (traces=13 evals=30287) + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345406) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_17 (traces=13 evals=25237) +[ ] - extrinsic_L3_18 (traces=13 evals=22195) +[ ] - extrinsic_L3_19 (traces=11 evals=17919) +[ ] - extrinsic_L3_22 (traces=17 evals=22712) +[ ] - extrinsic_L3_20 (traces=14 evals=22656) +[ ] - extrinsic_L3_21 (traces=14 evals=31584) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_23 (traces=17 evals=12656) +[ ] - extrinsic_L3_24 (traces=15 evals=37579) +[ ] - extrinsic_L3_25 (traces=13 evals=25029) +[ ] - extrinsic_L3_26 (traces=14 evals=31264) +[ ] - extrinsic_L3_27 (traces=17 evals=29475) +[ ] - extrinsic_L3_28 (traces=14 evals=25823) + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_29 (traces=12 evals=13802) +[ ] - extrinsic_L4_1 (traces=17 evals=18576) +[ ] - extrinsic_L4_3 (traces=17 evals=26949) +[ ] - extrinsic_L4_2 (traces=8 evals=17794) +[ ] - extrinsic_L4_4 (traces=17 evals=24606) +[ ] - extrinsic_L4_5 (traces=17 evals=29438) +[ ] - extrinsic_L4_6 (traces=14 evals=29013) +[ ] - extrinsic_L4_7 (traces=17 evals=32048) +[ ] - extrinsic_L4_9 (traces=17 evals=25875) +[ ] - extrinsic_L4_8 (traces=15 evals=23520) +[ ] - extrinsic_L4_10 (traces=8 evals=10627) +[ ] - extrinsic_L4_11 (traces=11 evals=22730) +[ ] - extrinsic_L4_12 (traces=15 evals=22751) +[ ] - extrinsic_L4_13 (traces=11 evals=49962) +[ ] - extrinsic_L4_14 (traces=9 evals=28124) +[ ] - extrinsic_L5_1 (traces=17 evals=24289) + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_2 (traces=16 evals=18747) + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345407) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_3 (traces=14 evals=29813) + +thread '' (1345403) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=15 evals=28862) +[ ] - extrinsic_L5_7 (traces=17 evals=27842) +[ ] - extrinsic_L5_5 (traces=3 evals=30536) +[ ] - extrinsic_L5_6 (traces=17 evals=19980) +[ ] - extrinsic_L5_8 (traces=17 evals=19802) + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345410) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=13 evals=34162) +[ ] - extrinsic_L5_10 (traces=11 evals=29462) +[ ] - extrinsic_L6_2 (traces=17 evals=20349) +[ ] - extrinsic_L5_11 (traces=7 evals=51904) +[ ] - extrinsic_L6_1 (traces=11 evals=17334) +[ ] - extrinsic_L6_3 (traces=1 evals=737) +[ ] - extrinsic_L6_4 (traces=17 evals=23952) +[ ] - extrinsic_L6_5 (traces=11 evals=58843) +[ ] - extrinsic_L6_6 (traces=9 evals=4392) +[ ] - extrinsic_L6_8 (traces=17 evals=22785) +[ ] - extrinsic_L6_7 (traces=8 evals=9772) +[ ] - extrinsic_L6_9 (traces=8 evals=18083) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 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0000000000000000000000000000000000000000..fe4818e43251b277ef0a347b778fa8f5660e26b3 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s45/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070930-irhpe4f8 +[2026-06-29T07:09:27.217938] Seeded RNGs with seed=45 +[2026-06-29T07:09:27.218215] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-29T07:09:30.769721] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json + 526 training examples loaded. + +============================================================ +[2026-06-29T07:09:30.770844] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 526 -> 526 unique examples + Epoch 1/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 18 total steps, 526 unique examples (batch_size=64) +[2026-06-29T07:09:34.652340] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:34.659162] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s45/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 18} diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/summary.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..cfecdcd55ac115464ffdb900dfc684d40565f77b --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + 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prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ['A -> 'A]])); (not [('A : prop) -> ['A -> 'A]]).", + "a not_i", + "=> [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 556, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [false -> [x -> x]]; [(not false) -> [x -> x]].", + "a or_e", + "=> [false -> [false -> [x -> x]]]; [(not false) -> [false -> [x -> x]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [x -> x]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> [false -> [x -> x]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [x -> x]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> [false -> [x -> x]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal3).", + "c em", + "=> (em p@type@2).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 494, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> false]; [(not [('A : prop) -> ['A -> 'A]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]; [(not [('A : prop) -> ['A -> 'A]]) -> [[('A : prop) -> ['A -> 'A]] -> false]].", + "a or_e", + "=> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> [[('A : prop) -> ['A -> 'A]] -> false]]]; 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(and 'A 'B) -> 'B]))))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))))].", + "intro.", + "a not_i", + "=> [(not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 554, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]); [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false].", + "intro.", + "a x", + "=> (and [false -> ('P : prop) -> 'P] false).", + "a and_i", + "=> false.", + "a x", + "=> (and [[('A : 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"=> (em goal13).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))).", + "a x", + "=> (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))).", + "a x", + "=> (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))))).", + "a x", + "=> (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))))).", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))))))).", + "a or_e", + "=> [(and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) -> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))))))]; [(not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) -> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))))))].", + "a x", + "=> (and (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))))) [(and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) -> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) (and (or (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) (not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)))) (and false (and (and [false -> ('P : prop) -> 'P] false) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))))))))]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) false).", + "c em", + "=> (em goal7).", + "a and_i", + "=> (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)); false.", + "a and_i", + "=> (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false); (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false)) -> false]; [(not (and (and (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false) (and [[('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] -> false] false)) (and [('P : prop) -> ['P -> false] -> (not 'P)] false))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 510, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a x0", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em false).", + "c not_e", + "=> (not_e not_e@type x1 not_e).", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]].", + "a x1", + "=> (iff [false -> ('P : prop) -> 'P] [(or [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] (not [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B])) -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal12).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 325, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> 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-> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> 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'Q) -> 'Q]) -> [[false -> ('P : prop) -> 'P] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 42, + "evals_used": 1273, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and x 'B) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and x 'B) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : 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false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1637, + "actions": [ + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]; [(not [false -> ('P : prop) -> 'P]) -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal0).", + "a x", + "=> false.", + "c em", + "=> (em goal11).", + "a x", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]) -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]) -> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "c em", + "=> (em goal17).", + "a x", + "=> false.", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 p0@type goal p0 and_i).", + "c x1", + "=> (x1 goal exfalso@type and_i exfalso).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1711, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]) -> false].", + "c x", + "=> (x or_ir@type or_ir@type or_ir or_ir).", + "intro.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el or_ir@type or_ir@type p5).", + "c x0", + "=> (x0 exfalso@type and_er@type exfalso and_er).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2095, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal goal16 and_i).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1532, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4457, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> 'B -> (and x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> 'B -> (and x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) 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prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)))]].", + "intro.", + "a x", + "=> (iff (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> (or 'P (not 'P))] false) (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 522, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p1@type).", + "intro.", + "a or_e", + "=> [(or false (not false)) -> false]; [(not (or false (not false))) -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a or_e", + "=> [(or false (not false)) -> (and [('P : prop) -> (not 'P) -> 'P -> false] false)]; [(not (or false (not false))) -> (and [('P : prop) -> (not 'P) -> 'P -> false] false)].", + "c em", + "=> (em goal7).", + "a x", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] [(or false (not false)) -> (and 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-> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "a exfalso", + "=> false.", + "a x", + "=> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) false).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) false)]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) false)].", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and (not (or [('P : prop) 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-> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x", + "=> (x goal goal15 x).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + 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-> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + 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false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and x [false -> [false -> false]]).", + "a and_i", + "=> x; [false -> [false -> false]].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4577, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (or x 'B)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (or x 'B)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type p0@type x1 p0).", + "c and_el", + "=> (and_el not_e@type p0@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x2", + "=> (x2 not_e@type not_e@type x1 x1).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x2", + "=> (x2 or_ir@type or_il@type or_ir or_il).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x2", + "=> (x2 exfalso@type goal exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c x2", + "=> (x2 p10@type not_e@type p10 not_e).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 576, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))); (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> false].", + "intro.", + "c x0", + "=> (x0 p3@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 435, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c 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'A 'B)]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]).", + 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: prop) -> (iff 'A 'B) -> ['A -> 'B]] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2186, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 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and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : 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-> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('B : prop) -> (iff x 'B) -> [x -> 'B]]); [('B : prop) -> (iff x 'B) -> [x -> 'B]].", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + 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: prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type iff_er@type iff_er).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])) 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not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not false) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [false -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not false) -> [false -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 659, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff x 'B) -> ['B -> 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not_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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false]].", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 407, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not 'A) -> 'A -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (not 'A) -> 'A -> false]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> 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or_e", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6856, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]]].", + "c x0", + "=> (x0 or_e@type p0@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])].", + "c x0", + "=> (x0 or_ir@type p2@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10968, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not x) -> x -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]].", + "c x0", + "=> (x0 not_e@type goal not_e not_e).", + "c and_el", + "=> (and_el not_e@type not_e@type p3).", + "c em", + "=> (em p2@type@2).", + "c x1", + "=> (x1 iff_i@type or_ir@type iff_i or_ir).", + "c and_el", + "=> (and_el not_e@type goal p3).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]].", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 exfalso@type and_i@type exfalso x1).", + "c x1", + "=> (x1 exfalso@type not_i@type exfalso not_i).", + "c x0", + "=> (x0 and_i@type and_er@type x1 and_er).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not x) -> x -> false]]]]].", + "c x1", + "=> (x1 or_ir@type p3@type or_ir p3).", + "a exfalso", + "=> false.", + "a p4", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c x0", + "=> (x0 goal and_el@type not_e and_el).", + "c x1", + "=> (x1 p2@type p6@type p2 p6).", + "c x1", + "=> (x1 p13@type p11@type p13 p11).", + "c x0", + "=> (x0 and_er@type p1@type and_er p1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2587, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not 'A) -> 'A -> false]); [('A : prop) -> (not 'A) -> 'A -> false].", + "a not_i", + "=> [[('A : prop) -> (not 'A) -> 'A -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_e@type or_e).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not (not [('A : prop) -> (not 'A) -> 'A -> false]))); (not (not [('A : prop) -> (not 'A) -> 'A -> false])).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [(not (not [('A : prop) -> (not 'A) -> 'A -> false])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11 exfalso@type exfalso).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + 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['B -> 'A] -> (iff 'A 'B)]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]))) -> false].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p4@type@2 exfalso@type exfalso).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c x0", + "=> (x0 em@type not_i@type not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]]); [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]]]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4265, + "actions": [ + "intro.", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> 'B] -> ['B -> x] -> (iff x 'B)]].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> 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prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "c x0", + "=> (x0 p0@type exfalso@type p0 exfalso).", + "c and_er", + "=> (and_er p0@type exfalso@type p4).", + "c and_el", + "=> (and_el not_i@type and_i@type p2).", + "a not_e", + "=> (not (and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a p6", + "=> [(and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c and_er", + "=> (and_er not_i@type and_i@type x1).", + "c and_el", + "=> (and_el p0@type exfalso@type p4).", + "c p7", + "=> (p7 p@type em@type p em).", + "c p7", + "=> (p7 iff_er@type exfalso@type iff_er p5).", + "c p7", + "=> (p7 p2@type p0@type x1 p0).", + "a p5", + "=> false.", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_il@type and_i@type or_il p7).", + "c em", + "=> (em goal2).", + "c x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 711, + "actions": [ + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal10).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x", + "=> (x not_i@type p3@type not_i p3).", + "c and_er", + "=> (and_er not_i@type p3@type p4).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal11).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p6@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em p4@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "intro.", + "c x1", + "=> (x1 not_e).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "c em", + "=> (em goal0@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(not x) -> false]; [(not (not x)) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or x (not x))); (or x (not x)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or x (not x)))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or x (not x)))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3617, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (or 'A (not 'A))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> (or 'A (not 'A))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a x", + "=> (not (or x0 (not x0))); (or x0 (not x0)).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [(or x0 (not x0)) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "c x1", + "=> (x1 not_i@type false not_i).", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal5).", + "c x1", + "=> (x1 p@type goal p).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [false -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "c x1", + "=> (x1 p3@type and_i@type p3).", + "c x2", + "=> (x2 or_il@type x3).", + "c em", + "=> (em p4@type).", + "c x1", + "=> (x1 p0@type not_e@type p0).", + "c x3", + "=> (x3 x1).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 441, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false]; [(not [('A : prop) -> (or 'A (not 'A))]) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x0", + "=> (x0 goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1480, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x goal or_e@type em).", + "c x", + "=> (x iff_i@type and_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_e@type not_i@type not_e).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('A : prop) -> (or 'A (not 'A))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('A : prop) -> (or 'A (not 'A))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> (or 'A (not 'A))]); [('A : prop) -> (or 'A (not 'A))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> (or 'A (not 'A))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> (or 'A (not 'A))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2315, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (or 'A (not 'A))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (or 'A (not 'A))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a 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'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not x) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not (not x)) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 954, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em goal17).", + "c and_er", + "=> (and_er exfalso@type and_el@type p5).", + "a p8", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a p6", + "=> false.", + "c x0", + "=> (x0 exfalso@type and_el@type p5)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[x -> false] -> (not x)]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "intro.", + "c em", + "=> (em p@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p4@type@2).", + "a x0", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1062, + "actions": [ + "c em", + "=> (em or_ir@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[x -> false] -> (not 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: prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 goal2 p0@type p0).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3573, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ['A -> false] -> (not 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ['A -> false] -> (not 'A)]].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ['A -> false] -> (not 'A)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('A : prop) -> ['A -> false] -> (not 'A)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "c x", + "=> (x goal iff_el@type not_i iff_el).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x iff_er@type goal x0 not_i).", + "c x", + "=> (x goal p2@type not_i p2).", + "c em", + "=> (em goal6).", + "c x", + "=> (x or_il@type and_el@type or_il and_el).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "c and_el", + "=> (and_el goal p6@type p4).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c and_er", + "=> (and_er goal or_ir@type p4).", + "c x2", + "=> (x2 goal p2@type p4).", + "c x", + "=> (x p7@type iff_i@type p7 iff_i).", + "a x2", + "=> (and [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x2", + "=> (and (and [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c and_er", + "=> (and_er goal false p4).", + "c x1", + "=> (x1 or_il@type and_el@type p6).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (and (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 359, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))) -> false].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (not (not [('P : prop) -> 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false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ['A -> false] -> (not 'A)]); [('A : prop) -> ['A -> false] -> (not 'A)].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]].", + "intro.", 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "intro.", + "c em", + "=> (em p6@type).", + "intro.", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 540, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em p@type@2).", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)].", + "c em", + "=> (em p0@type@2).", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]; [(not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]).", + "a and_i", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]).", + "c em", + "=> (em and_el@type).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "intro.", + "c not_e", + "=> (not_e and_er@type x0 and_er).", + "a x", + "=> (and (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2274, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C]); [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : 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-> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 627, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x 'B) -> [x -> 'C] -> ['B -> 'C] -> 'C]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x 'B) -> [x -> 'C] -> ['B -> 'C] -> 'C]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x 'B) -> [x -> 'C] -> ['B -> 'C] -> 'C]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (or x 'B) -> [x -> 'C] -> ['B -> 'C] -> 'C]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not false)].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not false)]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not false)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [[('P : prop) -> ('Q : 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-> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 296, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 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['P -> 'Q]] -> false]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (iff false (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (iff false (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> (not (not x))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [x -> (not (not x))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : 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(x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1963, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> 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or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 297, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P 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'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not x2); x2.", + "a exfalso", + "=> false.", + "a x1", + 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-> (or 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em goal).", + "a x", + "=> (iff (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a iff_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2241, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]]) -> false].", + "intro.", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false]); [[('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] -> false].", + "c x0", + "=> (x0 p1@type p6@type@2)." + ] + } + ], + "problem": "extrinsic_L1_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 18885, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 344, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P 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[[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em p1@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 390, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] -> [(or [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])) -> false]]; [(not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]]) -> [(or [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])) -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> 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"=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2161, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 297, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [false -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> false]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [false -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> [(not x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em 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iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> [(not x) -> 'B]]]]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 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false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4194, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type@2 not_e@type not_e).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> 'Q 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prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]])].", + "a exfalso", + "=> false.", + "c x", + "=> (x not_e@type em@type em).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P 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"c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) 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[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x1", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 506, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ['B -> ['A -> 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-> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 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-> (not 'P)]) -> false]].", + "intro.", + "c x1", + "=> (x1 p3@type and_er@type p3 and_er).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x1 x0).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> 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prop) -> (not 'P) -> 'P -> false])) -> false].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "c em", + "=> (em goal3).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))); (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false]].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "c x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2624, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> 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-> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c x1", + "=> (x1 exfalso@type em@type exfalso em).", + "c and_er", + "=> (and_er exfalso@type em@type p5).", + "intro.", + "c x1", + "=> (x1 em@type exfalso@type em x0).", + "c x1", + "=> (x1 iff_el@type p2@type iff_el p2).", + "c and_el", + "=> (and_el exfalso@type em@type p5).", + "a x0", + "=> false.", + "a p9", + "=> false.", + "c and_er", + "=> (and_er em@type exfalso@type p7).", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a p9", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3630, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c 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false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 416, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + 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or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", 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em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1798, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p1@type or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 297, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2440, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type or_ir).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 goal12 or_il@type or_il).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c x0", + "=> (x0 p2@type em@type em).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4293, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type iff_i@type p0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P 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or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> 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('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "c not_e", + "=> (not_e not_e@type x0 not_e).", + "a exfalso", + "=> .", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]; [(not [false -> ('P : prop) -> 'P]) -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a x", + "=> (and [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] [[false -> ('P : prop) -> 'P] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] [[false -> ('P : prop) -> 'P] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]])]; [(not [false -> ('P : prop) -> 'P]) -> (and [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] [[false -> ('P : prop) -> 'P] -> [(not (not 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prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]])]].", + "a x", + "=> (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> (and [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] [[false -> ('P : prop) -> 'P] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]])]]).", + "c em", + "=> (em goal14).", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] (and (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) [[('P : prop) -> (or 'P (not 'P))] -> [[false -> ('P : prop) -> 'P] -> (and [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]] [[false -> ('P : prop) -> 'P] -> [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 452, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c 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'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "a x0", + "=> (and (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))) false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5204, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em 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-> 'P]))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]))).", + "a and_i", 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-> 'R] -> 'R] -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false] (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] -> false] (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]) -> false] (not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]))))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + 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+ "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + 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-> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P 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'Q)])) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) (not [false -> ('P : prop) -> 'P])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [false -> ('P : prop) -> 'P]) -> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c 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false]]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 630, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [['C -> x] -> ['C -> 'B]]]]; [(not [('P : prop) -> 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-> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false]] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> 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-> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])) -> false]; (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[false -> ('P : prop) -> 'P] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]])] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) 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or_e", + "=> [(not false) -> false]; [(not (not false)) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 468, + "actions": [ + "c em", + "=> (em not_e@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> 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-> 'P -> (or 'P 'Q)] -> (and false [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) false)])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1685, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + 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: prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1458, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "a x4", + "=> (or x [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [x -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_il", + "=> x.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (and (not x) x) -> 'B]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (and (not x) x) -> 'B]]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 557, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]].", + "c em", + "=> (em p2@type).", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])).", + "a x1", + "=> (and [('P : prop) -> (or 'P (not 'P))] (and [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> (or 'P (not 'P))] (and [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> (or 'P (not 'P))] (and [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> (or 'P (not 'P))] (and [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [('A 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('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]].", + "a or_e", + "=> [[[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> [[[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> [[[[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]]; [(not [[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]) -> [[[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> [[[[false -> ('P : prop) -> 'P] -> [('A : prop) -> (iff (and 'A 'A) 'A)]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]]].", + "intro.", + "c em", + "=> (em goal19).", + "a x", + "=> false.", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 x).", + "c p5", + "=> (p5 p0@type).", + "c iff_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 359, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A 'A) 'A)] -> false]; [(not [('A : prop) -> (iff (and 'A 'A) 'A)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c iff_er", + "=> (iff_er p5@type@1 not_i@type p5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1402, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6907, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> (iff (and 'A 'A) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> (iff (and 'A 'A) 'A)]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> (iff (and 'A 'A) 'A)])); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> (iff (and 'A 'A) 'A)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x x) -> x]; [x -> (and x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> false])].", + "a x1", + "=> (iff (not [false -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [false -> (iff (not [false -> false]) [('P : prop) -> ('Q : prop) 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('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(or x x) -> x]]]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [(or x x) -> x]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] false).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] false)]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] false)].", + "c em", + "=> (em goal0@1).", + "c x3", + "=> (x3 p5@type).", + "intro.", + "c em", + "=> (em goal11).", + "c not_e", + "=> (not_e iff_el@type x4 iff_el).", + "c x1", + "=> (x1 iff_el@type x4 x0).", + "a exfalso", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4523, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c and_er", + "=> (and_er em@type iff_i@type p4).", + "c x2", + "=> (x2 p@type and_i@type p and_i).", + "c x2", + "=> (x2 iff_el@type iff_er@type iff_el iff_er).", + "c x2", + "=> (x2 p5@type and_el@type p5 and_el).", + "a p8", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 447, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and (or [('A : prop) -> (iff (or 'A 'A) 'A)] (not [('A : prop) -> (iff (or 'A 'A) 'A)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (or [('A : prop) -> (iff (or 'A 'A) 'A)] (not [('A : prop) -> (iff (or 'A 'A) 'A)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (or [('A : prop) -> (iff (or 'A 'A) 'A)] (not [('A : prop) -> (iff (or 'A 'A) 'A)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x", + "=> (and [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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"=> [('A : prop) -> (iff (or 'A 'A) 'A)].", + "c x0", + "=> (x0 not_e@type goal not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('A : prop) -> (iff (or 'A 'A) 'A)] false)); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]; [(or [('A : prop) -> (iff (or 'A 'A) 'A)] false) -> [('A : prop) -> (iff (or 'A 'A) 'A)]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('A : prop) -> (iff (or 'A 'A) 'A)] false))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (or [('A : prop) -> (iff (or 'A 'A) 'A)] false))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(or x x) -> x]; [x -> (or x x)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff (or x x) x)); (iff (or x x) x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (iff (or x x) x))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (iff (or x x) x))].", + "a x1", + "=> (iff (not (iff (or x x) x)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff (not (iff (or x x) x)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff (not (iff (or x x) x)) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2485, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", 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-> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 p0@type and_i@type p0 and_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el p0@type and_i@type p2).", + "c x0", + "=> (x0 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(or 'P 'Q)])) -> (and [('P : prop) -> (not 'P) -> 'P -> false] [(or x x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])].", + "intro.", + "a x2", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> (not 'P) -> 'P -> false] [(or x x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])).", + "a or_e", + "=> [x -> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> (not 'P) -> 'P -> false] [(or x x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]))]; [x -> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> (not 'P) -> 'P -> false] [(or x x) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]))].", + "c em", + "=> (em goal).", + "c x1", + "=> (x1 em@type p4@type em).", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [x -> (and (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and [('P : prop) -> (not 'P) -> 'P -> false] 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prop) -> (iff (or 'A 'A) 'A)]].", + "a or_e", + "=> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]]; [(not [('A : prop) -> (iff (or 'A 'A) 'A)]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [[('A : prop) -> (iff (or 'A 'A) 'A)] -> [('A : prop) -> (iff (or 'A 'A) 'A)]]]]]; 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false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]]; [[(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false] -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 479, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x 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(and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]).", + "c em", + "=> (em not_e@type).", + "c and_er", + "=> (and_er x false x0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "c em", + "=> (em p2@type).", + "intro.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])).", + "a exfalso", + "=> .", + "a exfalso", + "=> .", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])]).", + "a and_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]])].", + "intro.", + "c x1", + "=> (x1 x false x0).", + "c not_e", + "=> (not_e not_e@type x2 not_e).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> .", + "intro.", + "c not_e", + "=> (not_e and_er@type x1 and_er).", + "a exfalso", + "=> .", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 567, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (iff (and x false) false)); (iff (and x false) false).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [(iff (and x false) false) -> false].", + "intro.", + "c iff_er", + "=> (iff_er goal0@1 false x0).", + "c iff_el", + "=> (iff_el goal0@1 false x0).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('A : prop) -> (iff (and 'A false) false)] -> false]; [(not [('A : prop) -> (iff (and 'A false) false)]) -> false].", + "c em", + "=> (em goal9).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p8@type).", + "a exfalso", + "=> false.", + "a p4", + "=> (and x false).", + "a p3", + "=> false.", + "a not_e", + "=> (not (or (not [('A : prop) -> (iff (and 'A false) false)]) (not (not [('A : prop) -> (iff (and 'A false) false)])))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> (and x false)] (not [false -> (and x false)]))).", + "a not_i", + "=> [(or [false -> (and x false)] (not [false -> (and x false)])) -> false].", + "a or_e", + "=> [[[('A : prop) -> (iff (and 'A false) false)] -> false] -> [(or [false -> (and x false)] (not [false -> (and x false)])) -> false]]; [(not [[('A : prop) -> (iff (and 'A false) false)] -> false]) -> [(or [false -> (and x false)] (not [false -> (and x false)])) -> false]].", + "intro.", + "c em", + "=> (em p5@type).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 524, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [(and x false) -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [(and x false) -> false]]]].", + "intro.", + "c em", + "=> (em not_i@type).", + "intro.", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) [(and x false) -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)].", + "c em", + "=> (em goal0@1).", + "c x3", + "=> (x3 p5@type).", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)].", + "a x0", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (iff [('P : prop) -> ['P -> false] -> (not 'P)] false)).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4518, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] 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or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [false -> ('P : prop) -> 'P]) -> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> (iff (and 'A false) false)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> false] (not [[('P : prop) -> (or 'P (not 'P))] -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false])); [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a x", + "=> (or false [('P : prop) -> ['P -> false] -> (not 'P)]); [false -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 310, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a iff_i", + "=> [(and x false) -> false]; [false -> (and x false)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])].", + "a x1", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2628, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x0", + "=> (x0 p0@type and_i@type p0 and_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el p0@type and_i@type p2).", + "c x0", + "=> (x0 iff_el@type p2@type 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2158, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + 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'R]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> x -> (iff 'B (and x 'B))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> x -> (iff 'B (and x 'B))]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p8", + "=> (p8 not_e@type iff_el@type not_e iff_el).", + "c x1", + "=> (x1 and_i@type and_i@type x1 p8).", + "c x0", + "=> (x0 not_e@type p@type not_e p).", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 and_er@type p12@type and_er p12).", + "c em", + "=> (em p3@type@2).", + "c x1", + "=> (x1 p10@type p@type p10 p).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p15@type and_i@type p15 p8).", + "c x1", + "=> (x1 and_el@type and_er@type and_el and_er).", + "c and_er", + "=> (and_er not_e@type p@type p13)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 550, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [false -> ('P : prop) -> 'P])]; [(not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c x0", + "=> (x0 goal11).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a or_e", + "=> [[(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [false -> ('P : prop) -> 'P])] -> false]; [(not [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [false -> ('P : prop) -> 'P])]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))); (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (not (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))].", + "intro.", + "a not_i", + "=> [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 674, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))]]].", + "c em", + "=> (em 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false]]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)].", + "intro.", + "a x0", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false) (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)).", + "a x", + "=> (and (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false) (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false) (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false) (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))) (and (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : 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-> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> x]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) 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-> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "c em", + "=> (em goal0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> (not (not [('P : prop) -> 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prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> x0])]]).", + "a and_i", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> x0])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> x0])]].", + "a x1", + "=> (and [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> x0])]] [x0 -> x0]).", + "a x1", + "=> (and (and [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x0 -> x0])]] [x0 -> x0]) [x0 -> x0]).", + "a exfalso", + "=> false.", + "a x", + "=> (not (and (not [x0 -> x0]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (and (not [x0 -> x0]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x" + ] + } + ], + "problem": "extrinsic_L2_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 11, + "evals_used": 22414, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 531, + "actions": [ + 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[(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]]]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]]].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : 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prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]]]]]; [(not (not x)) -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[x -> [(iff x x0) -> (iff x0 x)]] -> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> false]]]]]]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])); (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12898, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [(or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal6).", + "a x", + "=> (or false (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))); [false -> false]; [(or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or false (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (or false (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))].", + "a x", + "=> (or (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : 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-> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or false (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))].", + "a x", + "=> (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))))); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(or (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> .", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]); [[false -> ('P : prop) -> 'P] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> false].", + "c em", + "=> (em p@type).", + "a or_il", + "=> .", + "intro.", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not 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'P]])) -> (or (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or false (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]; [(not (or (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))) -> (or false (not (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2728, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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not_e", + "=> (not [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]); [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c not_e", + "=> (not_e p0@type x2 p0).", + "a x1", + "=> (or (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [false -> ('P : prop) -> 'P]) -> (not [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false])].", + "c em", + "=> (em goal9).", + "a or_ir", + "=> .", + "c x0", + "=> (x0 p4 p3@type@2).", + "c not_e", + "=> (not_e and_el@type p5 and_el)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2400, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> 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goal6 p4).", + "c em", + "=> (em p5@type).", + "c x3", + "=> (x3 x1).", + "c x3", + "=> (x3 or_il).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [[[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not 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prop) -> ['P -> false] -> (not 'P)])))) -> false]].", + "a x0", + "=> (or [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false] -> (or (not [('P : prop) -> (or 'P (not 'P))]) [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false])]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> (or 'P (not 'P))]) [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false])].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] -> (or [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false] -> false].", + "a x0", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) (or (not [('P : prop) -> (or 'P (not 'P))]) [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false])); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false])]; [(or (not [('P : prop) -> (or 'P (not 'P))]) [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false])].", + "a or_ir", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) [(or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 408, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> 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or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 554, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2305, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + "=> false.", + "a x0", + 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-> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c x1", + "=> (x1 iff_i@type).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 goal10).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [('P : 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exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not false)]; [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]]; [[('P : prop) -> ('Q : prop) 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 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[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", 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[[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6406, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 iff_i@type em@type em).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 goal iff_er@type iff_er).", + "c x0", + "=> (x0 goal p0@type p0).", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> (or [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "c x0", + "=> (x0 exfalso@type or_ir@type x0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> 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+ "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 628, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [x -> 'B] -> [(not 'B) -> (not x)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('B : prop) -> [x -> 'B] -> [(not 'B) -> 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+ "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c p8", + "=> (p8 em@type p9@type p9).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + 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prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal3).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))).", + "a or_e", + "=> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]; [(not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> (not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))))]]].", + "intro.", + "c em", + "=> (em goal18).", + "c x", + "=> (x and_i@type x1 and_i).", + "a exfalso", + "=> .", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal10).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> false].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]); [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]].", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2135, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x false not_e@type not_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x goal11 p0@type p0).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8690, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> [x -> (not 'B)] -> ['B -> (not x)]]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c em", + "=> (em p3@type).", + "c x1", + "=> (x1 exfalso@type p@type exfalso p).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] 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false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false]].", + "a x", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false]]).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and [('P : prop) -> ['P -> false] -> (not 'P)] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)).", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]] -> false] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 498, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]])); (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]).", + "a or_e", + "=> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]; [(not false) -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))].", + "a or_e", + "=> [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]]; [(not false) -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]] -> [[false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]]) -> [[false -> [false -> (not (not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]))]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]].", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]]) -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> [[('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] -> false]]].", + "c em", + "=> (em p8@type@2).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 45, + "evals_used": 1406, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1529, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (or (not false) [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]); [(not false) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_il", + "=> (not false).", + "a not_i", + "=> [false -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 529, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(and x 'C) -> (and 'B 'C)]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal7).", + "c em", + "=> (em p3@type).", + "c em", + "=> (em p8@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2628, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type x0).", + "a not_e", + "=> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false]))); (not (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] -> false].", + "intro.", + "c x1", + "=> (x1 em).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type or_e@type or_e).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 660, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em 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('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]])) -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [false -> ('P : prop) -> 'P]) -> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6089, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[false -> ('P : prop) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 334, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and (or false (not false)) [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 635, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> 'B] -> [(or x 'C) -> (or 'B 'C)]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : 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prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]])].", + "c em", + "=> (em goal15).", + "c p3", + "=> (p3 p7@type).", + "c em", + "=> (em p8@type).", + "a p4", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or [x0 -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))] -> (or [x0 -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a p4", + "=> (or (not x0) (not (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]])))) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 298, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> 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"=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x1", + "=> false.", + "a not_e", + "=> (not [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]); [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]])]; [(not [false -> ('P : prop) -> 'P]) -> (not [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]])].", + "a x1", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (and [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]] false).", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a x1", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 411, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x and_er@type p3 and_er).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, 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exfalso", + "=> false.", + "a not_e", + "=> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]); [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a not_i", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> false] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> 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false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : 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exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x", + "=> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 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(or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]].", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]].", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal5).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]]]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]]]; [(not [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]]]]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]]]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]]]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> [[[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]] -> false]; [(not [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 424, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em goal).", 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-> (or 'P 'Q)])]].", + "intro.", + "a x", + "=> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]).", + "c em", + "=> (em p0@type@2).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))]]; [[('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "c em", + "=> (em and_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 560, + "actions": [ + "c em", + "=> (em em@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] 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[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> false]; [(not [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]) -> false].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1738, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type iff_er@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "c x", + "=> (x goal11 or_ir@type or_ir).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e and_i@type x1 and_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false]); [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 500, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not x) -> 'B]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em goal2).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 548, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [(not [('P : prop) -> (or 'P (not 'P))]) -> false]); [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> (not [(not [('P : prop) -> (or 'P (not 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-> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 450, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] 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false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false]) -> [[[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]] -> false] -> [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]); [x0 -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em p0@type).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false].", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])) -> false].", + "a x", + "=> (or false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]).", + "a or_il", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1408, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + 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em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6991, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]]); [[false -> ('P : prop) -> 'P] -> false]; [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]); [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] -> [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]]; [[[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false] -> [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false])]; [[(or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]] -> (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or false (not false)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false (not false)))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or false 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-> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or x 'B) -> [(not 'B) -> x]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal2).", + "c em", + "=> (em goal).", + "intro.", + "intro.", + "a not_e", + "=> (not 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not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] -> false]; 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false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x0", + "=> (or [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal18).", + "c em", + "=> (em goal16).", + "c em", + "=> (em goal15).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [false -> [false -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> ('C : prop) -> [x -> 'C] -> ['B -> 'C] -> [(or x 'B) -> 'C]]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 540, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> 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(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]] (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "intro.", + "c em", + "=> (em p5@type@2).", + "c em" + ] + }, + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])))]]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])))]]]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))])))]]]].", + "c x2", + "=> (x2 and_i).", + "c x1", + "=> (x1 p0@type@2).", + "c x1", + "=> (x1 goal16).", + "c em", + "=> (em goal20).", + "c em", + "=> (em p@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 710, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> 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false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x0", + "=> (x0 not_i@type p2@type not_i p2).", + "c and_er", + "=> (and_er not_i@type p2@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3571, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "c em", + "=> (em or_e@type).", + "a and_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c x0", + "=> (x0 not_e@type goal18 not_e).", + "c x0", + "=> (x0 exfalso@type or_il@type exfalso).", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))).", + "a x", + "=> (and (and [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false] (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c x0", + "=> (x0 or_ir@type and_er@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a 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('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 628, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (or x (and x 'B)) x)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (or x (and x 'B)) x)]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a iff_i", + "=> [(or x (and x x2)) -> x]; [x -> (or x (and x x2))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [(or x (and x x2)) -> x]); [(or x (and x x2)) -> x].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or x (and x x2)) -> x])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [(or x (and x x2)) -> x])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or x (and x x2)) -> x])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [(or x (and x x2)) -> x])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4985, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a not_i", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em goal9).", + "intro.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x0", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] x); [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [x -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_ir", + "=> x.", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (not [('P : prop) -> (or 'P (not 'P))])); [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> x]; [(not [('P : prop) -> (or 'P (not 'P))]) -> x].", + "c em", + "=> (em and_el@type).", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (not [('P : prop) -> (or 'P (not 'P))]))]; [[(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] -> (or [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_ir", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 675, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em 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-> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)))].", + "intro.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) false)))).", + "c em", + "=> (em iff_el@type).", + "a x" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P 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(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x", + "=> (x or_e@type and_er@type or_e).", + "a not_e", + "=> (not (not false)); (not false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not (not false))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "c x", + "=> (x p6@type goal19 p6).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 968, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; 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false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x2", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> false] false).", + "c em", + "=> (em not_i@type).", + "a x1", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; false.", + "c x1", + "=> (x1 exfalso@type iff_el@type exfalso iff_el).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el exfalso@type iff_el@type p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal20)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 938, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P 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[false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a not_i", + "=> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))].", + "intro.", + "a x0", + "=> false.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a and_i", + "=> false.", + "a x0", + "=> false.", + "a x3", + "=> (not [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false]); [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false].", + "a not_i", + "=> [[[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> false] -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "a x3", + "=> (not (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]])); (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4446, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false].", + "intro.", + "a x", + "=> (not false); false.", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "c x1", + "=> (x1 iff_i@type p@type@2).", + "c iff_el", + "=> (iff_el p1@type@1 iff_i@type p1).", + "c em", + "=> (em goal10).", + "c em", + "=> (em p0@type@2).", + "c x1", + "=> (x1 p1@type@1 p1@type@1@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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-> 'R])]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "c x2", + "=> (x2 p0@type p4@type p0 p4).", + "c x2", + "=> (x2 em@type p5@type em p5).", + "c x2", + "=> (x2 p4@type p@type p4 p).", + "c em", + "=> (em goal13).", + "c iff_er", + "=> (iff_er p1@type@1 iff_i@type p1)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 445, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c x", + "=> (x not_i@type).", + "intro.", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> false].", + "c x", + "=> (x goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])] -> (not [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1624, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c x", + "=> (x and_i@type iff_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a x0", + "=> (and [false -> false] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c x", + "=> (x p@type goal14 p).", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal14).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1039, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not false) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [false -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not false) -> [false -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "c x4", + "=> (x4 p2@type iff_i@type iff_i).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 14852, + "actions": [ + 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(x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 p@type p2@type p2).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir x1).", + "c x1", + "=> (x1 not_i@type p5@type not_i p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false iff_el@type iff_el).", + "c x1", + "=> (x1 and_er@type p11@type and_er p11).", + "c p9", + "=> (p9 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4@1@2).", + "c p4", + "=> (p4 x p1@type p1).", + "c p4", + "=> (p4 p1@type p@type p).", + "c p9", + "=> (p9 p8@type and_i@type p8 x1).", + "c p9", + "=> (p9 p17@type p17@type p17 p17).", + "c p4", + "=> (p4 or_ir@type p5@type p5).", + "c and_er", + "=> (and_er and_er@type p11@type p14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 542, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> false]].", + "intro.", + "c em", + "=> (em p5@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2076, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false 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[[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type or_ir@type p5 or_ir).", + "c and_er", + "=> (and_er p5@type or_ir@type p7).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c p8", + "=> (p8 goal not_i@type not_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 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'P) -> 'P -> false] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em goal5).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "c em", + "=> (em x0).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "a x1", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])); (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 406, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + 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+ "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[false -> ('P : prop) -> 'P] -> false] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[false -> ('P : prop) -> 'P] -> false] [false -> ('P : prop) -> 'P])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not false)]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2058, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal16).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 297, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> false]); [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [false -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [false -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [false -> false])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [false -> false]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [false -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x1 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> [x -> 'B] -> [x -> (not 'B)] -> (not x)]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false].", + "c x2", + "=> (x2 or_il@type p6@type or_il p6).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2439, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type or_ir@type x0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "c x0", + "=> (x0 goal12 or_il@type or_il).", + "a not_i", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type em@type em).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a not_e", + "=> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (or 'P (not 'P))]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 498, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal15).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "intro.", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 386, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> 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and_er@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p2@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a x0", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]." + ] + } + ], + "problem": "extrinsic_L3_18" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 12, + "evals_used": 17290, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 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'P]]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))]]].", + "a or_e", + "=> [(or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))]]]]; [(not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (not (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))))]]]].", + "c x2", + "=> (x2 p0@type goal14 p0).", + "c x2", + "=> (x2 iff_er@type goal14 iff_er).", + "c x2", + "=> (x2 p5@type goal7 p5).", + "a x1", + "=> (iff (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (or (or (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [('P : 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('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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(not 'P))] -> false]) -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e not_i@type x1 not_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 1386, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il" + ] + } + ], + "problem": "extrinsic_L3_19" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 6, + "evals_used": 11060, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 345, + "actions": [ + "intro.", + "a 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"c em", + "=> (em iff_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "intro.", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1390, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [(or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]] -> (or (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (or false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c x0", + "=> (x0 or_ir@type p0@type@2 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 373, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a not_e", + "=> (not (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))); (not (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 640, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (or x (or 'B 'C)) -> (or (or x 'B) 'C)]]; [(not [('P : prop) 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-> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))].", + "a x", + "=> (and [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])) (or (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) (and (and (and false [[('P : prop) 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 618, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em p@type).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x0", + "=> (iff (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]].", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))].", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))]]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))]].", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal18).", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (iff [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))]]))] (not [('P : prop) -> (not 'P) -> 'P -> false])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 966, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c em", + "=> (em or_il@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em x).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c x1", + "=> (x1 iff_i@type iff_el@type x2 iff_el).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 463, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P 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prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a exfalso", + "=> .", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 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[[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]]]]; [(not (or [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]))) -> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]]]].", + "intro.", + "c em", + "=> (em p4@type@2).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3875, + 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prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "a exfalso", + 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-> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a or_ir" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6215, + "actions": [ + "c em", + "=> 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(not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c x1", + "=> (x1 or_e@type exfalso@type or_e exfalso).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c x1", + "=> (x1 em@type em@type em em).", + "c and_er", + "=> (and_er em@type em@type p2).", + "c and_el", + "=> (and_el or_e@type exfalso@type p1).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a p4", + "=> (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q 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-> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [false -> ('P : prop) -> 'P])].", + "a p4", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P])].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 401, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> false].", + "a x", + "=> (or (and [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]) (and (not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false])).", + "a or_il", + "=> (and [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]).", + "a and_i", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false].", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]]; [(not [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]) -> [[('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] -> false]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1339, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type or_e@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 46, + "evals_used": 1909, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p)." + ] + } + ], + "problem": "extrinsic_L3_23" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 23863, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 521, + "actions": [ + "intro.", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(iff x (not x)) -> false]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]].", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(iff x (not x)) -> false]]]]]]].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> (iff 'A (not 'A)) -> false])); (not [('A : prop) -> (iff 'A (not 'A)) -> false]).", + "a not_i", + "=> [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false]); [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false].", + "a not_i", + "=> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]]); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> false] -> false]].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 445, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] (not [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (or [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] (not [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]))) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 12132, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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+ "=> (iff_er x x0@type@2 x0).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> 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prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 889, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> 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-> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "c em", + "=> (em or_e@type).", + "a x0", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; false.", + "c x0", + "=> (x0 not_e@type iff_er@type not_e iff_er).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el not_e@type iff_er@type p5).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "a x1", + "=> (and [false -> ('P : prop) -> 'P] [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false]).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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false]; [(not false) -> false].", + "c em", + "=> (em goal9).", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em p3@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])); (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]).", + "a not_i", + "=> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not 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prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> (iff 'A (not 'A)) -> false]]]]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]].", + "c x0", + "=> (x0 em@type p7@type p7).", + "a or_e", + "=> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> (iff 'A (not 'A)) -> false]]]] -> [[(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('A : prop) -> (iff 'A (not 'A)) -> false]]]] -> [(not [('P : prop) -> 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-> (and 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em or_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 447, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a x0", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x1", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a x1", + "=> false.", + "a x0", + "=> false.", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 or_ir@type).", + "a x0", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x1", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4374, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c x2", + "=> (x2 p@type or_e@type p or_e).", + "c x2", + "=> (x2 iff_er@type and_i@type iff_er and_i).", + "c x2", + "=> (x2 p5@type or_il@type p5 or_il).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]).", + "a p8", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 342, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) -> false].", + "a x0", + "=> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 507, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]].", + "a or_e", + "=> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]; [(not x) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "a or_e", + "=> [x -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]]; [(not x) -> [x -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7513, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) -> false]; [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]]; [(or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]]) [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])]] (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))].", + "c x0", + "=> (x0 or_ir@type goal19 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 296, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a x0", + "=> (iff false false).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 618, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> [x -> ['B -> 'C]] -> [(not (not x)) -> [(not (not 'B)) -> (not (not 'C))]]]].", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal9).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2441, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> 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prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c x1", + "=> (x1 or_e@type goal0 or_e).", + "a exfalso", + "=> false.", + "a x", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 p@type x0 p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> 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'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]]; [x0 -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]]].", + "c x2", + "=> (x2 em@type and_i@type em and_i).", + "c x2", + "=> (x2 iff_i@type iff_i@type iff_i iff_i).", + "c x2", + "=> (x2 p2@type or_il@type p2 x1).", + "c x1", + "=> (x1 p4@type iff_er@type p4).", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 337, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]); [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x0", + "=> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and [[false -> ('P : prop) -> 'P] -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 504, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2191, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not x)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] [false -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (not (not [x -> 'B])) -> [(not (not x)) -> (not (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]]); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]].", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]] -> false].", + "c x2", + "=> (x2 or_il@type p7@type or_il p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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not_i", + "=> [[('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + 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false]].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [false -> (not [false -> ('P : prop) -> 'P])]; [(not false) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 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-> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> false].", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal5).", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "c em", + "=> (em goal15).", + "c x", + "=> (x iff_er@type x2 iff_er).", + "a exfalso", + "=> .", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p2@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 407, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + 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'P]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]))) -> false].", + "a x", + "=> (and [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))])) -> false] [false -> ('P : prop) -> 'P]).", + "a and_i", + "=> [(or [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ 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'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false])); (not [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7175, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> false].", + "a x", + "=> (or [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal9 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]]); [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))].", + "c x0", + "=> (x0 or_ir@type goal18 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 341, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 505, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> ('C : prop) -> (not (not [x -> 'B])) -> (not (not ['B -> 'C])) -> (not (not [x -> 'C]))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))])); (not [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))]).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal3).", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2485, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> 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-> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c x0", + "=> (x0 p4@type@2 and_el@type and_el).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c x0", + "=> (x0 goal11 exfalso@type exfalso).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4311, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('A : prop) -> ('B : 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em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7583, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 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'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 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-> (or 'P 'Q)] -> false]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c x0", + "=> (x0 not_e@type p@type not_e).", + "c x0", + "=> (x0 not_e@type goal11 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [(not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]) -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [[(not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]) -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 544, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (iff (not (not (and x 'B))) (and (not (not x)) (not (not 'B))))]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))]) -> false].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] -> false]]; [(not false) -> [[('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and 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prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not (not 'A)))]); [('A : prop) -> (iff 'A (not (not 'A)))].", + "a exfalso", + "=> false.", + 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or false (not false)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or false (not false)))].", + "a x1", + "=> (iff (not (or 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : 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['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)]))]]).", + "c em", + "=> (em goal24).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('P : prop) -> ['P -> false] -> (not 'P)] false)]))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 409, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c and_er", + "=> (and_er em@type iff_i@type p4).", + "c x2", + "=> (x2 p@type and_i@type p x).", + "c x2", + "=> (x2 iff_el@type em@type iff_el em).", + "c x2", + "=> (x2 p5@type and_el@type p5 and_el).", + "a p8", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])).", + "c p2", + "=> (p2 em@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]; [(not [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]) -> false].", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]].", + "intro.", + "c em", + "=> (em not_e@type).", + "intro.", + "a x1", + "=> .", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false] -> false]]].", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type iff_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p1@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not false)]; [(or [false -> ('P : prop) -> 'P] [('P : prop) -> (or 'P (not 'P))]) -> (not false)].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6089, + "actions": [ + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]].", + "c x0", + "=> (x0 iff_i@type em@type em).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 goal or_ir@type or_ir).", + "c x0", + "=> (x0 goal or_e@type or_e).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> (or 'P (not 'P))]))].", + "c x0", + "=> (x0 not_e@type p4@type p4)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 335, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : 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-> 'R])) (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (and [false -> ('P : prop) -> 'P] false) (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) false)))].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [false -> ('P : prop) -> 'P] false) (and (or [('P : prop) -> ('Q : prop) 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x0", + "=> false.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 iff_er@type p3@type p3).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 493, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) 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-> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", 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['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1393, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type iff_er@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type goal11 not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) 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-> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "c x0", + "=> (x0 iff_el@type iff_i@type iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [false -> ('P : prop) -> 'P]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] -> false]]; [[false -> ('P : prop) -> 'P] -> [[[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 p@type@2 iff_el@type iff_el).", + "c x0", + "=> (x0 p@type@2 em@type em).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [[('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] -> false])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : 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-> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + 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['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]).", + "c em", + "=> (em goal23).", + "a x0", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]] [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) x) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])]]) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1652, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> 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[('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))) [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c em", + "=> (em p8@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1371, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + 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-> ('P : prop) -> 'P])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "c x3", + "=> (x3 goal14 and_er@type and_er).", + "intro.", + "a x0", + "=> false.", + "a not_e", + "=> (not [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]); [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2743, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not (not [('P : 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prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "intro.", + "intro.", + "c not_e", + "=> (not_e and_i@type x3 x2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c x2", + "=> (x2 em@type and_i@type em x2).", + "c x2", + "=> (x2 iff_i@type or_il@type iff_i or_il).", + "c x2", + "=> (x2 p0@type p@type p0 p).", + "c em", + "=> (em goal13).", + "a exfalso", + "=> ." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1471, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]])) -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false]; [(not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 em@type goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 496, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (not false)) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [false -> ('P : prop) -> 'P]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [[(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false] -> [[false -> ('P : prop) -> 'P] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]) -> [[false -> ('P : prop) -> 'P] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1856, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]); [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x false not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c x0", + "=> (x0 or_e@type em@type or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em 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-> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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-> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 577, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]].", + "a or_e", + "=> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]; [(not false) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]]; [(not false) -> [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]]); [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [false -> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]])]; [(not false) -> (not [false -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> [(not (and x 'B)) -> (or (not x) (not 'B))]]]]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [false -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [false -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em p3@type).", + "c em", + "=> (em p9@type@2).", + "c em", + "=> (em or_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2625, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type and_el@type 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('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]).", + "c em", + "=> (em goal19).", + "a x1", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]) (and (not x) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]])).", + "a x1", + "=> (and (and (not x) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]) (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]]) (and (not x) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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'P 'Q) -> 'Q]))))]]) (and (not x) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))))]])).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 378, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not 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-> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> false].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p4@type or_e@type p4 or_e).", + "c and_er", + "=> (and_er p4@type or_e@type p6).", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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-> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a or_ir", + "=> .", + "c em", + "=> (em goal4).", + "c em", + "=> (em p2@type@2).", + "intro.", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not (not [('P : prop) -> ('Q : prop) 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"a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]))).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))]; [[false -> ('P : prop) -> 'P] -> (not (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 46, + "evals_used": 1888, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]]); [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : 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(or x [x -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (or x [x -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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-> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "c em", + "=> (em goal19).", + "a or_e", + "=> [(iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]; [(not (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]].", + "a exfalso", + "=> false.", + "a x", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x3", + "=> (x3 and_el@type).", + "a or_e", + "=> 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-> (iff 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1358, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2018, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "c not_e", + "=> (not_e iff_el@type x1 iff_el).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [false -> ('P : prop) -> 'P])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [false -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "intro.", + "c em", + "=> (em goal19).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not false) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4275, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or x [x -> 'B])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or x [x -> 'B])]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em p1@type@2).", + "c x2", + "=> (x2 not_e@type iff_er@type x0 iff_er).", + "c and_el", + "=> (and_el not_e@type iff_er@type p3).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x2", + "=> (x2 or_il@type p6@type or_il p6).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1389, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x0", + "=> (x0 goal12).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x1", + "=> (x1 goal11 exfalso@type exfalso).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p0@type).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4308, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal1).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type iff_el@type p0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x", + "=> (x exfalso@type p1@type@2 exfalso).", + "c x", + "=> (x em@type or_e@type em).", + "a exfalso", + "=> false.", + "c x", + "=> (x p0@type p@type p0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "c x", + "=> (x or_ir@type p2@type or_ir).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 304, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", 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-> (not 'P) -> 'P -> false] -> false]]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]] -> [x0 -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]] -> false]); [[[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]] -> false].", + "a exfalso", + "=> false.", + "a x2", + "=> (not [x0 -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]); [x0 -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "c x3", + "=> (x3 x1).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal11).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] false).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; false.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "c x", + "=> (x em@type not_i@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5591, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or false (not [('P : prop) -> (not 'P) -> 'P -> false])); [false -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or false (not [('P : prop) -> (not 'P) -> 'P -> false])) (or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]))); [(or false (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(or [[('P : prop) -> (not 'P) -> 'P -> false] -> false] (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> (or false (not [('P : prop) -> (not 'P) -> 'P -> false])).", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x0", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or false (not [('P : prop) -> (not 'P) -> 'P -> false]))]] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]] [false -> [false -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [false -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 651, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [x -> (not x)]) -> x]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [x 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em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1386, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2081, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c x", + "=> (x and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> false] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em 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-> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> [false -> false]]].", + "intro.", + "a x4", + "=> (or (or false (not false)) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or false (not false)) -> [false -> [false -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [false -> [false -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [false -> [(or false (not false)) -> [false -> [false -> false]]]]; [(not false) -> [(or false (not false)) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10525, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (or [x -> 'B] ['B -> x])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (or [x -> 'B] ['B -> x])]].", + "c x0", + "=> (x0 not_i@type and_er@type not_i and_er).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "c and_el", + "=> (and_el not_i@type and_er@type p1).", + "c em", + "=> (em goal4).", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c x0", + "=> (x0 not_i@type p6@type p4 p6).", + "c p7", + "=> (p7 not_e@type and_i@type not_e p7).", + "c x1", + "=> (x1 and_i@type and_i@type x1 x1).", + "c x0", + "=> (x0 not_e@type and_er@type not_e and_er).", + "a exfalso", + "=> false.", + "c p7", + "=> (p7 and_er@type p5@type and_er p5).", + "c em", + "=> (em 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-> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false]].", + "c p11", + "=> (p11 not_i@type).", + "intro.", + "c and_el", + "=> (and_el iff_el@type em@type p7).", + "intro.", + "a p10", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 520, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [false -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [false -> false]].", + "intro.", + "c em", + "=> (em goal1).", + "a or_e", + "=> [(not false) -> [false -> false]]; [(not (not false)) -> [false -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [false -> false]].", + "a exfalso", + "=> false.", + "c x", + "=> (x p1@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x", + "=> (x goal5).", + "a not_e", + "=> (not [(not false) -> [false -> false]]); [(not false) -> [false -> false]].", + "c em", + "=> (em goal).", + "c x", + "=> (x p3@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p5@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [(not false) -> [false -> false]])); (not [(not false) -> [false -> false]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 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prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p5@type and_er@type and_er).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c x1", + "=> (x1 goal not_e@type not_e).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1189, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false)).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))].", + "a x2", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))]).", + "a x2", + "=> (and [false -> ('P : prop) -> 'P] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))])).", + "c em", + "=> (em goal11).", + "a x2", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) (and [false -> ('P : prop) -> 'P] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false))]))).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]].", + "intro.", + "c em", + "=> (em goal18).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]])).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (or 'P (not 'P))] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]]).", + "c x3", + "=> (x3 iff_er@type iff_i@type iff_er iff_i).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1613, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x", + "=> (x not_i@type goal8).", + "intro.", + "c iff_el", + "=> (iff_el p5@type@1 p5@type@2 p5).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[false -> ('P : prop) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[false -> ('P : prop) -> 'P] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[false -> ('P : prop) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]); [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false] (not [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [(or [('P : 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-> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "intro.", + "a or_ir", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "a or_il", + "=> .", + "c x0", + "=> (x0 em@type or_ir@type or_ir).", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em and_el@type).", + "a x" + ] + } + ], + "problem": "extrinsic_L5_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 14, + "evals_used": 26300, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 899, + "actions": [ + "c em", + "=> (em em@type).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]].", + "a or_e", + "=> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]; [(not false) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]].", + "c em", + "=> (em p1@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal1).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]].", + "a or_e", + "=> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> (iff (and 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'A 'B))]]]] -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]]]]; [(not [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]) -> [[false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [false -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]]]]]]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em p14@type@2).", + "c em", + "=> (em p14@type).", + "c em", + "=> (em p17@type@2).", + "c em", + "=> (em p19@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (not [('P : prop) -> (or 'P (not 'P))]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (not [('P : prop) -> (or 'P (not 'P))]))] -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 594, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p5@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> false] [('P : prop) -> ['P -> false] -> (not 'P)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type goal exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]); [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7238, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]].", + "c x0", + "=> (x0 not_e@type p@type@2 not_e).", + "c x0", + "=> (x0 not_e@type goal13 not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [false -> ('P : prop) -> 'P])]]]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> (not 'P) -> 'P -> false])); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "c x0", + "=> (x0 or_ir@type p2@type or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1396, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not (not false))]; [(not false) -> (not (not false))].", + "a or_e", + "=> [false -> [false -> (not (not false))]]; [(not false) -> [false -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "intro.", + "a x4", + "=> (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (not 'P) -> 'P -> false]); [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_il", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : 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em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> (not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a 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-> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> 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prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 451, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em exfalso@type).", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not false) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "intro.", + "a or_e", + "=> [false -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]]; [(not false) -> [('B : prop) -> (iff (or (and x 'B) (and x (not 'B))) x)]].", + "c em", + 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: prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 323, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false]) -> false].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x2", + "=> .", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7320, + "actions": [ + 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prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a exfalso", + "=> false.", + "c em", + "=> (em 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'B))) 'A)]) -> false]; [(not (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)])) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + 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exfalso@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em goal14).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 295, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a or_e", + "=> [false -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [(not false) -> (iff [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4274, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]].", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x1", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q 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'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]])]]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]]]])]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x2", + "=> (x2 not_e@type not_i@type x1 not_i).", + "c em", + "=> (em false).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c x2", + "=> (x2 or_il@type p6@type or_il p6).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c x2", + "=> (x2 exfalso@type or_il@type exfalso or_il).", + "c em", + "=> (em goal3).", + "c x2", + "=> (x2 p2@type and_el@type p2 and_el).", + "c x2", + "=> (x2 p10@type not_e@type p10 x0).", + "c em", + "=> (em not_i@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 3682, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a or_ir", + "=> .", + "c em", + "=> (em p0@type).", + "intro.", + "a x1", + "=> .", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]].", + "a x0", + "=> (or (not [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> (or 'P (not 'P))]) -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]].", + "a or_il", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (not [('P : prop) -> (or 'P (not 'P))])]; [[[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]] -> (not [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em and_el@type).", + "a x0", + "=> (or (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]])].", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "c em", + "=> (em goal6).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)]); [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L5_4" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 7, + "evals_used": 16251, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 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false].", + "a or_il", + "=> .", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em goal5).", + "a x", + "=> (or false (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [false -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or false (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or false (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))].", + "a x", + "=> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]) (or (or (not [('P 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'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]) (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[false -> ('P : prop) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em goal1).", + "a or_ir", + "=> .", + "a x", + "=> (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) [('P : prop) -> (or 'P (not 'P))]); [(or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em p0@type@2).", + "a or_il", + "=> .", + "intro.", + "c em", + "=> (em goal6).", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [false -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]) (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)]; [(or (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> (not 'P) -> 'P -> false]) (or (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))) -> (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) false)]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 525, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + 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-> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[false -> ('P : prop) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em p5@type@2).", + "intro.", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x", + "=> false.", + "a x", + "=> false.", + "a x0", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))); (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 383, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : 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false]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 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+ "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_i).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 479, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : 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false).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (and (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) false)].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 623, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em em@type).", + "a not_i", + "=> [x -> false].", + "intro.", + "a exfalso", + "=> 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(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x and_er@type 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('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em not_i@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 494, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6727, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [[false -> ('P : prop) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 339, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not false) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [false -> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not false) -> [false -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "intro.", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 727, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('B : prop) -> (or (iff x 'B) (iff x (not 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(not [('P : prop) -> ['P -> false] -> (not 'P)])]])).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 382, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> 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-> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 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false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false].", + "intro.", + "a x0", + "=> (and x false).", + "a x0" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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"c x0", + "=> (x0 p0@type@2 em@type em).", + "c x0", + "=> (x0 p4@type@2 and_i@type and_i).", + "a not_e", + "=> (not (or (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or x (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em p7@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 412, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a 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-> (or 'P 'Q)])] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]].", + "intro.", + "c em", + "=> (em goal20).", + "c x2", + "=> (x2 x1).", + "c x", + "=> (x or_ir@type p3 or_ir).", + "c x2", + "=> (x2 x).", + "c x2", + "=> (x2 not_e).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 402, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]); [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]).", + "intro.", + "a or_e", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]) -> false]; [(not (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])])) -> false].", + "a x", + "=> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))])]) -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1415, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_el@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not (not [('P : prop) -> (not 'P) -> 'P -> false])); (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not (not [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6184, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c x0", + "=> (x0 or_e@type em@type x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]; [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false].", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))])); [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (or 'P (not 'P))]) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> (or (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or (not [('P : prop) -> (or 'P (not 'P))]) (not (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c x0", + "=> (x0 or_ir@type goal4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 356, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 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-> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 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-> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "a not_i", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e" + ] + } + ], + "problem": "extrinsic_L5_8" + }, + { + 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(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]].", + "a or_e", + "=> [x -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]]; [(not x) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]].", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal4).", + "a 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prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]]))).", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]] (not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]])) -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 803, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not 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: prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]]; [(not (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]))) -> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))])) -> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal19).", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a x", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 414, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal10).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [[false -> ('P : prop) -> 'P] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 534, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em p@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6404, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]].", + "c x0", + "=> (x0 or_e@type goal x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] -> false].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type or_e@type not_e).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 338, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + 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[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]))) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false]; [(not (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 539, + "actions": [ + 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'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]].", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em goal13).", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])] [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "c em", + "=> (em goal21).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not [('P : prop) -> ['P -> false] -> (not 'P)]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 357, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 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false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "intro.", + "a x2", + "=> .", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 679, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em em@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> 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false])).", + "a x0", + "=> (and (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 482, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em 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or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3615, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 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false]].", + "intro.", + "c x1", + "=> (x1 and_el@type p@type and_el p).", + "c em", + "=> (em goal6).", + "c and_er", + "=> (and_er and_el@type p@type p1).", + "c em", + "=> (em goal3).", + "c x1", + "=> (x1 p@type not_i@type p not_i).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 or_il@type and_er@type or_il and_er).", + "a x", + "=> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))); (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))))].", + "c and_el", + "=> (and_el or_il@type and_er@type p6).", + "intro.", + "c and_el", + "=> (and_el and_el@type p@type p1).", + "c p8", + "=> (p8 and_el@type p@type p1).", + "c p8", + "=> (p8 or_il@type and_er@type p6).", + "c x3", + "=> (x3 p5@type p0@type p5 p0).", + "c p8", + "=> (p8 p5@type p0@type p11).", + "c x3", + "=> (x3 p11@type not_e@type p11 x).", + "a p9", + "=> (and (not (not (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))))) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c p9", + "=> (p9 p@type not_i@type p12).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 352, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]))).", + "a not_i", + "=> [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "c em", + "=> (em goal12).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false] -> false]; [(not [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false]) -> false].", + "a x", + "=> false.", + "a or_e", + "=> [[(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false] -> false]; [(not [(or [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] (not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))])) -> false]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a x", + "=> false.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 506, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p1@type@2).", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [false -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [false -> false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [x -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]; [(not x) -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]].", + "a or_e", + "=> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]; [(not (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))) -> [x -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> [x -> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1859, + "actions": [ + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_i@type not_e@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x0", + "=> (x0 iff_i@type p@type p).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c x", + "=> (x p@type p2@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em goal15).", + "c em", + "=> (em p2@type).", + "a exfalso", + "=> false.", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1053, + "actions": [ + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not false))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not false))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not false))]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not false))]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [false -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]].", + "intro.", + "c x4", + "=> (x4 goal19 or_ir@type x4).", + "intro.", + "intro.", + "a or_e", + "=> [false -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]]]; [(not false) -> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [false -> [false -> false]]]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 15647, + "actions": [ + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('B : prop) -> (iff (or (and x (not 'B)) (and (not x) 'B)) (not (iff x 'B)))]].", + "c x0", + "=> (x0 not_i@type or_ir@type not_i or_ir).", + "c x0", + "=> (x0 and_i@type or_il@type and_i or_il).", + "intro.", + "intro.", + "c em", + "=> (em not_i@type).", + "a iff_i", + "=> [(or (and x (not x2)) (and (not x) x2)) -> (not (iff x x2))]; [(not (iff x x2)) -> (or (and x (not x2)) (and (not x) x2))].", + "c and_er", + "=> (and_er not_i@type or_ir@type p1).", + "c x0", + "=> (x0 not_e@type and_i@type not_e and_i).", + "c and_el", + "=> (and_el not_i@type or_ir@type p1).", + "c x0", + "=> (x0 p1@type p0@type p1 p0).", + "c p4", + "=> (p4 x not_i@type not_i).", + "c and_el", + "=> (and_el and_i@type or_il@type p2).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 or_ir@type and_i@type or_ir x1).", + "c x1", + "=> (x1 not_i@type p5@type not_i p5).", + "c p9", + "=> (p9 not_i@type p11@type p6 p11).", + "c p4", + "=> (p4 false em@type em).", + "c x1", + "=> (x1 and_er@type p11@type and_er p11).", + "c p9", + "=> (p9 or_il@type and_er@type or_il and_er).", + "c em", + "=> (em goal4@1@2).", + "c p4", + "=> (p4 goal1 p15@type p15).", + "c p4", + "=> (p4 goal4@1@1@2 or_il@type or_il).", + "c p9", + "=> (p9 p8@type and_i@type p8 x1).", + "c p9", + "=> (p9 p17@type p17@type p17 p17).", + "c p4", + "=> (p4 or_e@type or_e@type or_e).", + "c and_er", + "=> (and_er and_er@type p11@type p14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 553, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal3).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])]; [(not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))) -> (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a not_e", + "=> (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])); (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]).", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]) -> false].", + "intro.", + "c x0", + "=> (x0 p2@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]))); (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not (not (not [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]])))].", + "intro.", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 671, + "actions": [ + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]].", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]].", + "c em", + "=> (em exfalso@type).", + "intro.", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]].", + "a exfalso", + "=> false.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p1@type).", + "a and_i", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> false]].", + "a x", + "=> (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> false]]).", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]] -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)].", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)).", + "a x", + "=> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))]].", + "intro.", + "c em", + "=> (em iff_el@type).", + "a x", + "=> (and (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)] (and (not [('P : prop) -> ['P -> false] -> (not 'P)]) false)))]).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 42, + "evals_used": 298, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]; [(not [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))]) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]].", + "a or_e", + "=> [false -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]]; [(not false) -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em p@type@2).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]] -> [false -> false]]; [(not [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]]) -> [false -> false]].", + "c em", + "=> (em 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false].", + "a x0", + "=> (or [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal4).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "c x", + "=> (x p@type and_er@type p).", + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "c em", + "=> (em goal14).", + "c em", + "=> (em p1@type).", + "a exfalso" + ] + } + ], + "problem": 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-> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]].", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal1).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em goal2).", + "c em", + "=> (em false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> [[('P : prop) -> (or 'P (not 'P))] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)]]]]) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] -> false]].", + "a exfalso", + "=> false.", + "a 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: prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]).", + "a x0", + "=> (and (not [false -> ('P : prop) -> 'P]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false])).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [false -> ('P : prop) -> 'P]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]))).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false).", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false))]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> (and [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + 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['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x0", + "=> false.", + "c x2", + "=> (x2 p4@type or_ir@type or_ir).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 iff_er@type p5@type p5).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3633, + "actions": [ + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) 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: prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "intro.", + "c x", + "=> (x iff_er@type em@type iff_er em).", + "c and_er", + "=> (and_er iff_er@type em@type p1).", + "c x", + "=> (x iff_el@type p@type iff_el p).", + "c x", + "=> (x em@type iff_i@type p2 iff_i).", + "c em", + "=> (em p1@type).", + "c x", + "=> (x and_er@type p3@type and_er p3).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c and_el", + "=> (and_el and_er@type p3@type p6).", + "intro.", + "intro.", + "a not_e", + "=> (not [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [(and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]])].", + "c and_el", + "=> (and_el iff_el@type p@type p3).", + "a p9", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [(and [('P : prop) -> ('Q : prop) -> 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'P] -> false]]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] -> false]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c 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'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1412, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "c x", + "=> (x em@type exfalso@type em).", + "c x", + "=> (x exfalso@type em@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(or [('P : prop) -> (or 'P (not 'P))] [false -> ('P : prop) -> 'P]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [false -> ('P : prop) -> 'P])]; [[('P : prop) -> (or 'P (not 'P))] -> (not [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": 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[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> (not 'P) -> 'P -> false])]]].", + "c x0", + "=> (x0 or_e@type p@type@2 x).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a x", + "=> (or (or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) [('P : prop) -> (or 'P (not 'P))]); [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em and_er@type).", + "a or_il", + "=> .", + "c x0", + "=> (x0 not_i@type goal19 not_i).", + "c x0", + "=> (x0 not_e@type not_i@type not_e).", + "a x", + "=> (or [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[false -> ('P : prop) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[[false -> ('P : prop) -> 'P] -> false] -> (or [(or [[false -> ('P : prop) -> 'P] -> false] (not [[false -> ('P : prop) -> 'P] -> false])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x0", + "=> (x0 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 286, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [false -> [false -> false]]; [(not false) -> [false -> false]].", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "a or_e", + "=> [false -> [false -> [false -> [false -> false]]]]; [(not false) -> [false -> [false -> [false -> false]]]].", + "intro.", + "intro.", + "c em", + "=> (em goal).", + "a or_e", + "=> [false -> [false -> [false -> false]]]; [(not false) -> [false -> [false -> false]]].", + "a exfalso", + "=> .", + "intro.", + "a exfalso", + "=> .", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or false (not false)) -> [(not false) -> [false -> [false -> [false -> false]]]]]; [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> .", + "a or_e", + "=> [false -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]]; [(not false) -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [false -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [false -> [(not (or false (not false))) -> [(not false) -> [false -> [false -> [false -> false]]]]]]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a or_e", + "=> [(or false (not false)) -> [false -> false]]; [(not (or false (not false))) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [(or false (not false)) -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [(or false (not false)) -> [false -> false]]].", + "intro.", + "a x0", + "=> (and [false -> [false -> false]] [(or false (not false)) -> [false -> false]]).", + "a and_i", + "=> [false -> [false -> false]]; [(or false (not false)) -> [false -> false]].", + "a or_e", + "=> [(or false (not false)) -> [false -> [false -> false]]]; [(not (or false (not false))) -> [false -> [false -> false]]]." + ] + }, + { + "mode": "sample", + 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'C] -> ['C -> x] -> (iff x 'B)]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em goal0).", + "c em", + "=> (em em@type).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal1).", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 556, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "c em", + "=> (em goal4).", + "intro.", + "c x0", + "=> (x0 or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not x); x.", + "c x0", + "=> (x0 p4@type@2).", + "a not_i", + "=> [x -> false].", + "intro.", + "c x0", + "=> (x0 goal11).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 2068, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em or_e@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) false).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p2@type@2).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); false.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> false].", + "a or_e", + "=> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]; [(not (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]].", + "a x", + "=> (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]).", + "a x", + "=> (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])).", + "a exfalso", + "=> false.", + "a x", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)].", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> 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prop) -> (and 'P 'Q) -> 'Q]))) -> false]])) -> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) false)].", + "a x", + "=> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]))))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]))))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]))))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (and [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> false]]))))]].", + "intro.", + "c em" + ] + } + ], + "problem": "extrinsic_L6_1" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 3, + "evals_used": 70691, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 938, + "actions": [ + "c em", + "=> (em false).", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]; [(not false) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]].", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]; [(not [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]) -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]].", + "a or_e", + "=> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) 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(or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]]]; [(not [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]) -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [[false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]] -> [false -> [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))]]]]].", + "c em", + "=> (em goal).", + "c em", + "=> (em goal1).", + "c em", + "=> (em goal2).", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em p@type).", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em 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(or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])])) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 58, + "evals_used": 69349, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal12).", + 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[[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))].", + "intro.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not (or [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])))].", + "intro.", + "a not_i", + "=> [(or [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] (not [[('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])])) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 566, + "actions": 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false]].", + "intro.", + "c x1", + "=> (x1 goal8).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [false -> ('P : prop) -> 'P]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [false -> ('P : prop) -> 'P]) -> false]].", + "intro.", + "c em", + "=> (em or_e@type).", + "intro.", + "a x0", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x1 x0).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P 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('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x", + "=> (x em@type not_e@type em).", + "c x", + "=> (x exfalso@type iff_i@type exfalso).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c x", + "=> (x not_i@type p0@type not_i).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em goal11).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal14).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(or [('P : prop) -> (or 'P (not 'P))] [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 458, + "actions": [ + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 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+ "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x0", + "=> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]].", + "a x0", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "c em", + "=> (em goal4).", + "intro.", + "c em", + "=> (em goal10).", + "a x0", + "=> (and (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a and_i", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]])]]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 296, + "actions": [ + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]].", + "intro.", + "intro.", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a x0", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (iff [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3486, + "actions": [ + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em false).", + "intro.", + "intro.", + "c x", + "=> (x and_el@type p1@type and_el p1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "c em", + "=> (em em@type).", + "c and_el", + "=> (and_el and_el@type p1@type p2).", + "c x0", + "=> (x0 p1@type and_i@type p1 x).", + "a p4", + "=> (and [false -> false] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c and_el", + "=> (and_el p1@type and_i@type p5).", + "c em", + "=> (em p3@type@2).", + "a x0", + "=> [false -> false]; (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c x0", + "=> (x0 not_e@type not_i@type not_e not_i).", + "c p4", + "=> (p4 not_e@type not_i@type p8).", + "a p4", + "=> (and [false -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x0", + "=> [false -> false].", + "a exfalso", + "=> false.", + "a p9", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "c em", + "=> (em p0@type).", + "a p4", + "=> (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]).", + "c x0", + "=> (x0 iff_el@type and_el@type iff_el and_el).", + "c p4", + "=> (p4 p1@type and_i@type p5).", + "a p4", + "=> (and (and (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]) (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])))).", + "c x0", + "=> (x0 and_el@type or_ir@type p4 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1645, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false]; [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "c em", + "=> (em goal6).", + "intro.", + "c x0", + "=> (x0 not_i@type not_i@type not_i).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type).", + "a not_e", + "=> (not [[('P : prop) -> (or 'P (not 'P))] -> false]); [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x0", + "=> (x0 p4@type@2 or_il@type or_il).", + "a not_i", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> false].", + "intro.", + "c x1", + "=> (x1 em).", + "intro.", + "a not_e", + "=> (not (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 512, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em not_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false].", + "c em", + "=> (em p1@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]].", + "c em", + "=> (em p2@type@2).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal15).", + "a or_e", + "=> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "intro.", + "c x1", + "=> (x1 not_e@type x3 not_e).", + "c em", + "=> (em exfalso@type).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 379, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R 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: prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_il", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_ir", + "=> .", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em goal5).", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em p1@type).", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))]); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a x", + "=> (or (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (or (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "c em", + "=> (em goal2).", + "a or_ir", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))); [(or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))]) (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))))); [(or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))]) -> false]; [(or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (not (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))))) -> false].", + "c em", + "=> (em p0@type).", + "a or_il", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> (or 'P (not 'P))]).", + "a or_il", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 550, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "c em", + "=> (em iff_i@type).", + "a x0", + "=> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso", + "=> false.", + "a x0", + "=> (and false false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false].", + "intro.", + "c not_e", + "=> (not_e or_e@type x2 or_e).", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em goal21).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]] (and (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 882, + "actions": [ + "c em", + "=> (em and_er@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) false).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "intro.", + "c em", + "=> (em and_i@type).", + "a not_e", + "=> (not [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]); [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 iff_er@type or_ir@type iff_er or_ir).", + "a exfalso", + "=> false.", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "c x0", + "=> (x0 iff_er@type or_ir@type p4).", + "c em", + "=> (em goal14).", + "a and_i", + "=> false.", + "c and_er", + "=> (and_er iff_er@type or_ir@type p4).", + "c em", + "=> (em p6@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 662, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em iff_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em p1@type).", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a x0", + "=> (and (not (not [('P : prop) -> ['P -> false] -> (not 'P)])) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (not (not [('P : prop) -> ['P -> false] -> (not 'P)])) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false])).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (not (not [('P : prop) -> ['P -> false] -> (not 'P)])) [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]))).", + "a 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) false))].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c em", + "=> (em goal9)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 417, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> false]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) 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: prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 26, + "evals_used": 37408, + "actions": [ + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]); [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "c x1", + "=> (x1 or_il@type or_ir@type goal7).", + "c x1", + "=> (x1 p0@type@2 or_ir@type or_e@type)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..3806b693441b2e97675691940de79ae64951fe0d --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,953 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_4 (traces=17 evals=25116) +[ ] - extrinsic_L0_5 (traces=17 evals=26619) +[ ] - extrinsic_L0_6 (traces=17 evals=30254) +[ ] - extrinsic_L0_1 (traces=17 evals=18542) +[ ] - extrinsic_L0_3 (traces=13 evals=14479) +[ ] - extrinsic_L0_2 (traces=13 evals=29634) + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L0_10 (traces=5 evals=13958) + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_el [('A : prop) -> ['A -> false] -> (not 'A)] (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false])) (x [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] not_i (and_el [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (x [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] or_ir or_e)))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] (or [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]))) and value type (and [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) did not unify. + +thread '' (1345828) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) not_i (x [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] not_i iff_el))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) did not unify. +[ ] - extrinsic_L0_7 (traces=17 evals=20235) + +thread '' (1345828) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) not_i (x [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] not_i iff_el))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) did not unify. + +thread '' (1345828) panicked at src/universe/term.rs:872:33: +Ill-typed term (and_er [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (x [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) not_i (x [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] not_i iff_el))): parameter type (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) and value type (and [('A : prop) -> ['A -> false] -> (not 'A)] (and [('A : prop) -> ['A -> false] -> (not 'A)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) did not unify. +[ ] - extrinsic_L0_11 (traces=17 evals=23877) +[ ] - extrinsic_L0_8 (traces=15 evals=29297) +[ ] - extrinsic_L0_9 (traces=15 evals=31537) +[ ] - extrinsic_L0_13 (traces=17 evals=22035) +[ ] - extrinsic_L0_12 (traces=14 evals=25539) +[ ] - extrinsic_L1_3 (traces=17 evals=18885) +[ ] - extrinsic_L2_1 (traces=17 evals=14186) +[ ] - extrinsic_L0_14 (traces=14 evals=17159) +[ ] - extrinsic_L1_2 (traces=17 evals=24111) +[ ] - extrinsic_L1_1 (traces=14 evals=14806) +[ ] - extrinsic_L1_4 (traces=16 evals=24670) +[ ] - extrinsic_L2_3 (traces=17 evals=23305) +[ ] - extrinsic_L2_2 (traces=17 evals=26646) +[ ] - extrinsic_L2_5 (traces=17 evals=24235) +[ ] - extrinsic_L2_4 (traces=17 evals=25252) +[ ] - extrinsic_L2_6 (traces=17 evals=19832) +[ ] - extrinsic_L2_7 (traces=17 evals=21942) + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L2_8 (traces=17 evals=28864) +[ ] - extrinsic_L2_9 (traces=14 evals=25015) +[ ] - extrinsic_L2_10 (traces=17 evals=22700) +[ ] - extrinsic_L2_11 (traces=11 evals=20984) +[ ] - extrinsic_L2_12 (traces=11 evals=22414) +[ ] - extrinsic_L2_13 (traces=11 evals=17999) +[ ] - extrinsic_L3_1 (traces=11 evals=14900) +[ ] - extrinsic_L3_4 (traces=17 evals=26905) + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_2 (traces=13 evals=25712) +[ ] - extrinsic_L3_3 (traces=8 evals=9654) + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_5 (traces=17 evals=21985) + +thread '' (1345803) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_6 (traces=17 evals=21255) +[ ] - extrinsic_L3_7 (traces=17 evals=29939) +[ ] - extrinsic_L3_10 (traces=17 evals=25869) +[ ] - extrinsic_L3_11 (traces=17 evals=16214) +[ ] - extrinsic_L3_8 (traces=9 evals=20614) +[ ] - extrinsic_L3_9 (traces=15 evals=19710) + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_12 (traces=17 evals=27652) + +thread '' (1345802) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345802) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_15 (traces=17 evals=17592) +[ ] - extrinsic_L3_17 (traces=17 evals=25523) +[ ] - extrinsic_L3_13 (traces=17 evals=29738) +[ ] - extrinsic_L3_14 (traces=7 evals=15555) +[ ] - extrinsic_L3_16 (traces=16 evals=31712) + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_18 (traces=17 evals=20363) + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_21 (traces=17 evals=22915) +[ ] - extrinsic_L3_19 (traces=12 evals=17290) +[ ] - extrinsic_L3_20 (traces=6 evals=11060) +[ ] - extrinsic_L3_22 (traces=17 evals=19760) +[ ] - extrinsic_L3_24 (traces=17 evals=23863) +[ ] - extrinsic_L3_23 (traces=11 evals=17172) +[ ] - extrinsic_L3_27 (traces=17 evals=19378) +[ ] - extrinsic_L3_25 (traces=8 evals=10961) +[ ] - extrinsic_L3_26 (traces=17 evals=23945) +[ ] - extrinsic_L3_29 (traces=17 evals=24189) +[ ] - extrinsic_L3_28 (traces=17 evals=22341) +[ ] - extrinsic_L4_1 (traces=14 evals=18690) + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345804) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_2 (traces=15 evals=15892) + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=15 evals=32639) + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_7 (traces=17 evals=32220) + +thread '' (1345828) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_4 (traces=1 evals=693) +[ ] - extrinsic_L4_5 (traces=15 evals=29869) +[ ] - extrinsic_L4_6 (traces=15 evals=26159) +[ ] - extrinsic_L4_8 (traces=17 evals=24096) +[ ] - extrinsic_L4_10 (traces=17 evals=23183) + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_9 (traces=11 evals=22393) + +thread '' (1345799) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_13 (traces=17 evals=27115) +[ ] - extrinsic_L4_11 (traces=14 evals=22240) +[ ] - extrinsic_L4_12 (traces=15 evals=25060) +[ ] - extrinsic_L4_14 (traces=13 evals=30027) +[ ] - extrinsic_L5_1 (traces=17 evals=29078) +[ ] - extrinsic_L5_2 (traces=14 evals=26300) +[ ] - extrinsic_L5_3 (traces=17 evals=24811) +[ ] - extrinsic_L5_4 (traces=14 evals=22323) +[ ] - extrinsic_L5_5 (traces=7 evals=16251) + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345805) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_6 (traces=17 evals=24475) +[ ] - extrinsic_L5_8 (traces=17 evals=27270) +[ ] - extrinsic_L5_7 (traces=14 evals=21323) +[ ] - extrinsic_L5_9 (traces=15 evals=25939) +[ ] - extrinsic_L5_10 (traces=16 evals=27884) +[ ] - extrinsic_L5_11 (traces=11 evals=54745) +[ ] - extrinsic_L6_1 (traces=15 evals=22455) +[ ] - extrinsic_L6_4 (traces=9 evals=38257) +[ ] - extrinsic_L6_6 (traces=3 evals=1770) +[ ] - extrinsic_L6_3 (traces=1 evals=828) +[ ] - extrinsic_L6_5 (traces=9 evals=58996) +[ ] - extrinsic_L6_2 (traces=3 evals=70691) +[ ] - extrinsic_L6_7 (traces=17 evals=16119) +[ ] - extrinsic_L6_9 (traces=8 evals=49755) +[ ] - extrinsic_L6_8 (traces=3 evals=70507) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 1/94 in 9485.3s diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..a0914671065cc73295792b2e4196ba14cff85ba7 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 18 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_0pt/s46/train.log b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/train.log new file mode 100644 index 0000000000000000000000000000000000000000..5421abf2ac339bf2691d4906916acf6bee303445 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_0pt/s46/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070931-edw0u537 +[2026-06-29T07:09:27.278783] Seeded RNGs with seed=46 +[2026-06-29T07:09:27.279051] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/0.pt +[2026-06-29T07:09:30.783840] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_0pt/examples_policy_only.json + 526 training examples loaded. + +============================================================ +[2026-06-29T07:09:30.784970] Starting ablation: updates_0_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64 +============================================================ + Dedup: 526 -> 526 unique examples + Epoch 1/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/9 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 18 total steps, 526 unique examples (batch_size=64) +[2026-06-29T07:09:34.682965] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:34.689193] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/summary.json + updates_0_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_0pt/s46/2026-06-29_07-09-27/updates_0_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 18} diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/summary.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..7017d4bd6ecbcc9ffa5e2c728d9fb8c9c012eb2d --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + 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[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (iff false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (or x (not x))) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]; [[('A : prop) -> (or 'A (not 'A))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6320, + "actions": [ + "c em", + "=> (em and_i@type).", + "intro.", + "a or_ir", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not x)].", + "c em", + "=> (em goal6).", + "c x1", + "=> (x1 iff_i@type or_e@type iff_i or_e).", + "intro.", + "c and_er", + "=> (and_er iff_i@type or_e@type p4).", + "c x3", + "=> (x3 iff_er@type and_el@type iff_er and_el).", + "a or_e", + "=> [false -> (not x)]; [(not false) -> (not x)].", + "a or_e", + "=> [[('A 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-> false].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a not_e", + "=> (not (or x (not x))); (or x (not x)).", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or x (not x)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or x (not x)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "a not_e", + "=> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or x (not x)))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or x (not x)))].", + "a x1", + "=> (and (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or x (not x)))]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", 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and_i", + "=> (and (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or x (not x)))]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 437, + "actions": [ + "intro.", + "a or_il", + "=> x.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> x.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> x]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> x].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> x]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> x]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em false).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]].", + "intro.", + "c em", + "=> (em goal9).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em x).", + "c em", + "=> (em goal18).", + "intro.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1162, + "actions": [ + "intro.", + "a or_ir", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a 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em", + "=> (em goal18).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]) -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2510, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x0", + "=> (x0 or_il@type goal1 or_il).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : 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'Q)])]] (and x (or x0 x1)))).", + "a x5", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not x1)] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] (and x (or x0 x1)))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [x1 -> false]]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 358, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a and_i", + "=> x; (or x0 x1).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(and x x0) -> false]; [(and x x1) -> false].", + "intro.", + "a not_e", + "=> (not (and x (or x0 x1))); (and x (or x0 x1)).", + "a not_i", + "=> [(and x (or x0 x1)) -> false].", + "c and_el", + "=> (and_el x x0 x3).", + "intro.", + "c and_er", + "=> (and_er x goal0@2 x4).", + "a not_e", + "=> (not (or 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-> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em goal6).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c em", + "=> (em x1@type).", + "c x4", + "=> (x4 and_el@type not_e@type and_el).", + "c em", + "=> (em goal4).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a or_e", + "=> [[x -> x0] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [x -> x0]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c x4", + "=> (x4 p2@type goal5 p2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "c x5", + "=> (x5 x3).", + "c em", + "=> (em or_e@type).", + "c x1", + "=> (x1 x3).", + "c x4", + "=> (x4 iff_el@type not_e@type iff_el).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x6", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c x7" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2062, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> [[x -> x0] -> [(not x) -> x0] -> x0]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]].", + "intro.", + "a x1", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]].", + "intro.", + "a x1", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]) -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]].", + "a x1", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]) -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]].", + "a x1", + "=> [x -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]]]; [(not x) -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [x -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]]]]]].", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a x1", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x1", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))) -> false].", + "c x3", + "=> (x3 goal goal5 x2).", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 exfalso@type x0 exfalso).", + "a x2", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal12).", + "a x1", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a x2", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x1", + "=> [[[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]] -> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> [[x -> x0] -> [(not x) -> x0] -> x0]]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 540, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false].", + "intro.", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]); [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false].", + "a x1", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false])].", + "intro.", + "a x2", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] -> false].", + "a x0", + "=> (and [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a and_i", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a x", + "=> (not [('P : prop) -> ('Q : prop) -> ('R 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-> (not ['A -> (not 'A)]) -> 'A]))])))]).", + "c em", + "=> (em goal11@1).", + "a x1", + "=> (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]).", + "a x1", + "=> (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]).", + "a x1", + "=> (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]).", + "a x1", + "=> (not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]).", + "a x1", + "=> (not [(not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]))]).", + "a not_i", + "=> [[(not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]))] -> false].", + "a x1", + "=> (not [[[(not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]) -> (not (not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]))]))]) -> (not (not [(not [(not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]))]) -> (not (not [(not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]))]) -> (not (not [(not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])))]) -> (not (not [(not (not [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))])) -> (not (not (not 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(not (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]))]) -> (not [false -> (not false)])].", + "intro.", + "c em", + "=> (em goal10).", + "a x1", + "=> (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]).", + "a x1", + "=> (not [(not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]) -> (not (not [(not [false -> (not false)]) -> (not (not [false -> (not false)]))]))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 677, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> x].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] 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false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]].", + "c x2", + "=> (x2 p5@type@2).", + "c em", + "=> (em p8@type@2).", + "c x2", + "=> (x2 p4@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4006, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x", + "=> (x iff_i@type and_i@type and_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em em@type).", + "c x", + "=> (x and_i@type iff_er@type iff_er).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c x", + "=> (x and_el@type or_e@type or_e).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x", + "=> (x p2@type exfalso@type exfalso).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "c x1", + "=> (x1 iff_i@type em@type x0 em).", + "a exfalso", + "=> false.", + "c x", + "=> (x exfalso@type p@type p).", + "c x1", + "=> (x1 not_e@type or_e@type not_e or_e).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el not_e@type or_e@type p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + 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['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "c em", + "=> (em p3@type).", + "intro.", + "c em", + "=> (em goal8).", + "a x2", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) false).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a x2", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) false).", + "c em", + "=> (em p5@type@2).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [false -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em goal).", + "c em", + "=> (em p1@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c not_e", + "=> (not_e iff_el@type x4 iff_el).", + "c not_e", + "=> (not_e iff_el@type x4 x2).", + "a or_e", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "c em", + "=> (em p6@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not ['A -> (not 'A)]) -> 'A]); [('A : prop) -> (not ['A -> (not 'A)]) -> 'A].", + "a not_i", + "=> [[('A : prop) -> (not ['A -> (not 'A)]) -> 'A] -> false].", + "intro.", + "a x", + "=> (not [false -> (not false)]).", + "a not_i", + "=> [[false -> (not false)] -> false].", + "intro.", + "a x", + "=> (not [false -> (not false)]).", + "a not_i", + "=> [[false -> (not false)] -> false].", + "intro.", + "a not_e", + "=> (not false); false.", + "a x1", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[false -> (not false)] -> false]); [[false -> (not false)] -> false].", + "a not_i", + "=> [[[false -> (not false)] -> false] -> false].", + "intro.", + "c em", + "=> (em not_i@type).", + "c x2", + "=> (x2 x0).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x", + "=> (not [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x", + "=> (not [false -> (not false)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "a x", + "=> (not [[[false -> ('P : prop) -> 'P] -> false] -> (not [[false -> ('P : prop) -> 'P] -> false])]).", + "a not_i", + "=> [[[[false -> ('P 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(and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a x1", + "=> (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [x -> (not x)]).", + "a x1", + "=> (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [x -> (not x)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a x1", + "=> (and (and (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and (and [[('P : prop) -> (not 'P) -> 'P -> false] -> false] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [x -> (not x)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x3", + "=> (x3 iff_i@type not_e@type iff_i not_e).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 586, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> [x -> (not x)].", + "intro.", + "a not_i", + "=> [x -> false].", + "intro.", + "c em", + "=> (em x0@type@1).", + "a or_e", + "=> [[x -> (not x)] -> false]; [(not [x -> (not x)]) -> false].", + "a exfalso", + "=> false.", + "a x1", + "=> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) false)].", + "intro.", + "a x1", + 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: prop) -> (or 'P (not 'P))] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a or_ir", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em and_el@type).", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q 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prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]].", + "a x0", + "=> (or [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]); [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]]; [[('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a or_ir", + "=> .", + "intro.", + "a x", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [('P : 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not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a iff_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [('P : prop) -> (not 'P) -> 'P -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "intro.", + "a x0", + "=> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a iff_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [('P : prop) -> (not 'P) -> 'P -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em false).", + "a x", + "=> (and [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [('P : prop) -> (not 'P) -> 'P -> false]] (not false)).", + "c em", + "=> (em p@type).", + "a and_i", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] -> [('P : prop) -> (not 'P) -> 'P -> false]]; (not false).", + "c em", + "=> (em goal2).", + "a x0", + "=> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]).", + "a or_e", + "=> [false -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])]; [(not false) -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])].", + "a x", + "=> (and [false -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]).", + "a or_e", + "=> [false -> (and [false -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])]; [(not false) -> (and [false -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])].", + "a x0", + "=> (iff (and [false -> (iff [('P : prop) -> (not 'P) -> 'P -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]) false).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 608, + "actions": [ + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[[x -> x0] -> x] -> x]); [[[x -> x0] -> x] -> x].", + "a not_i", + "=> [[[[x -> x0] -> x] -> x] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a not_i", + "=> 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[(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(not (not [[[x -> x0] -> x] -> x])) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "a x4", + "=> (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]]).", + "a and_i", + "=> [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]].", + "a x4", + "=> (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x3", + "=> (and (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) x).", + "c em", + "=> (em goal20).", + "a x3", + "=> (and (and (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal22).", + "a x4", + "=> (and (and (and (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [[[x -> x0] -> x] -> x]))).", + "a x4", + "=> (and (and (and (and (and [(not [[[x -> x0] -> x] -> x]) -> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (not (not [[[x -> x0] -> x] -> x]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]].", + "a or_e", + "=> [[[[x -> x0] -> x] -> x] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]]]; [(not [[[x -> x0] -> x] -> x]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]]].", + "intro.", + "intro.", + "c x3", + "=> (x3 x1).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a x4", + "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff [('P : 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+ "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] false)).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 557, + "actions": [ + "intro.", + "intro.", + "intro.", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [false -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [false -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [false -> false]]].", + "intro.", + "a x3", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [false -> false]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "c em", + "=> (em goal8).", + "c em", + "=> (em p@type@2).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "c em", + "=> (em not_i@type).", + "a x3", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false).", + "c em", + "=> (em x1@type).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false)]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false)].", + "c em", + "=> (em or_il@type).", + "intro.", + "a iff_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false]; [false -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x2", + "=> (iff (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) false).", + "c em", + "=> (em p0@type).", + "c x4", + "=> (x4 goal13).", + "c x4", + "=> (x4 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-> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "intro.", + "c x3", + "=> (x3 x1@type).", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 and_er@type).", + "a not_e", + "=> (not [x -> x0]); [x -> x0].", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not x0); x0.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a x5", + "=> (iff x false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff x false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff x false)].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5166, + "actions": [ + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> 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(and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "c p8", + "=> (p8 or_il@type and_el@type p0).", + "a p1", + "=> (and false (not [false -> ('P : prop) -> 'P])).", + "c and_el", + "=> (and_el em@type iff_el@type p).", + "a p8", + "=> (and (and false (not [false -> ('P : prop) -> 'P])) [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 806, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_il", + "=> x.", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> x]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> x].", + "intro.", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x).", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)]].", + "intro.", + "a x4", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)]).", + "a x4", + "=> (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])).", + "a exfalso", + "=> false.", + "a x3", + "=> (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false).", + "a x4", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false)).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false))).", + "a x3", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false)) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false)))).", + "a x3", + "=> (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] (and (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false)) (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] false))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)]))); (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]].", + "intro.", + "c em", + "=> (em goal20).", + "a x3", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]).", + "a x3", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]])) (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]])).", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]])) (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]))).", + "a x5", + "=> (and (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]])) (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (and false (and [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] x)])))]]))) x0).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3112, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])]); [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])].", + "a not_i", + "=> [[[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false].", + "c em", + "=> (em or_e@type).", + "c x4", + "=> (x4 x2).", + "a or_e", + "=> [x -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [[x0 -> x1] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [x -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [x -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]].", + "intro.", + "intro.", + "c em", + "=> (em goal9).", + "c em", + "=> (em em@type).", + "a exfalso", + "=> false.", + "a x5", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> (or 'P (not 'P))]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_il", + "=> .", + "a x5", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a or_ir", + "=> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])]).", + "c em", + "=> (em p@type).", + "a not_i", + "=> [[[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])] -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> false].", + "c em", + "=> (em x0).", + "a or_e", + "=> [x -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]; [[x0 -> x1] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2778, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not x0)]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not x0)].", + "c x4", + "=> (x4 or_il@type x0 x4).", + "intro.", + "a exfalso", + "=> false.", + "c x4", + "=> (x4 x2@type x0 x2).", + "c x4", + "=> (x4 iff_i@type goal0 iff_i).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c x4", + "=> (x4 not_e@type goal1 not_e).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(or x [x0 -> x1]) -> false].", + "c em", + "=> (em p@type@2).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p5@type@2).", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 39, + "evals_used": 51680, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em x1).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "intro.", + "a or_e", + "=> [x1 -> false]; [(not x1) -> false].", + "intro.", + "c x4", + "=> (x4 false x1 x6).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c x5", + "=> (x5 x iff_er@type x).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..1de9081c1ba6521b62d13c82e5951277f5fd825f --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,856 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=413) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L1_3 (traces=2 evals=527) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] - extrinsic_L0_9 (traces=2 evals=514) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] - extrinsic_L1_2 (traces=3 evals=698) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L3_1 (traces=1 evals=27) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L1_1 (traces=3 evals=845) +[OK ] - extrinsic_L2_6 (traces=3 evals=619) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_5 (traces=3 evals=893) +[OK ] - extrinsic_L3_4 (traces=3 evals=1100) +[OK ] - extrinsic_L3_9 (traces=8 evals=4164) + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L2_13 (traces=9 evals=11007) +[OK ] - extrinsic_L3_11 (traces=3 evals=904) + +thread '' (1345417) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345415) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_2 (traces=17 evals=17811) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[ ] - extrinsic_L3_8 (traces=17 evals=31009) + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_14 (traces=3 evals=1111) +[ ] - extrinsic_L3_7 (traces=17 evals=15931) +[ ] - extrinsic_L0_12 (traces=17 evals=25354) +[OK ] - extrinsic_L3_18 (traces=3 evals=1009) + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_16 (traces=8 evals=9447) +[OK ] - extrinsic_L3_17 (traces=10 evals=8235) +[ ] - extrinsic_L3_10 (traces=13 evals=17251) +[ ] - extrinsic_L3_12 (traces=17 evals=29379) +[OK ] - extrinsic_L3_23 (traces=8 evals=5522) + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_20 (traces=17 evals=13683) +[ ] - extrinsic_L3_15 (traces=13 evals=34639) +[ ] - extrinsic_L3_21 (traces=17 evals=17791) +[ ] - extrinsic_L3_19 (traces=13 evals=12523) +[OK ] - extrinsic_L3_25 (traces=8 evals=11169) + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345418) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_22 (traces=13 evals=12778) +[ ] - extrinsic_L3_24 (traces=12 evals=13556) + +thread '' (1345415) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_26 (traces=11 evals=5725) +[ ] - extrinsic_L4_1 (traces=17 evals=16613) +[ ] - extrinsic_L3_27 (traces=17 evals=23188) + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=13 evals=24072) + +thread '' (1345415) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=17 evals=19702) +[ ] - extrinsic_L4_2 (traces=16 evals=31513) +[ ] - extrinsic_L3_29 (traces=2 evals=9613) +[ ] - extrinsic_L4_6 (traces=17 evals=18296) +[ ] - extrinsic_L4_5 (traces=17 evals=24062) +[ ] - extrinsic_L4_4 (traces=9 evals=31072) +[ ] - extrinsic_L4_7 (traces=13 evals=31099) +[ ] - extrinsic_L4_9 (traces=17 evals=30349) +[ ] - extrinsic_L4_8 (traces=10 evals=31817) +[ ] - extrinsic_L4_10 (traces=17 evals=29323) +[ ] - extrinsic_L4_11 (traces=13 evals=19210) +[ ] - extrinsic_L4_12 (traces=13 evals=34396) + +thread '' (1345412) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1345412) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345419) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_13 (traces=13 evals=33903) +[ ] - extrinsic_L4_14 (traces=15 evals=29575) +[ ] - extrinsic_L5_1 (traces=16 evals=42929) +[ ] - extrinsic_L5_2 (traces=15 evals=27200) +[ ] - extrinsic_L5_3 (traces=13 evals=23978) +[ ] - extrinsic_L5_4 (traces=14 evals=30449) + +thread '' (1345417) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345417) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1345415) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_6 (traces=17 evals=27077) +[ ] - extrinsic_L5_5 (traces=12 evals=30303) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_7 (traces=7 evals=22782) +[ ] - extrinsic_L5_8 (traces=3 evals=22704) +[ ] - extrinsic_L5_9 (traces=6 evals=24052) +[ ] - extrinsic_L5_10 (traces=4 evals=22211) +[OK ] g extrinsic_L6_6 (traces=1 evals=58) +[ ] - extrinsic_L5_11 (traces=12 evals=39128) +[ ] - extrinsic_L6_2 (traces=15 evals=28039) +[ ] - extrinsic_L6_3 (traces=13 evals=17644) +[ ] - extrinsic_L6_4 (traces=2 evals=82428) +[ ] - extrinsic_L6_5 (traces=3 evals=65008) +[ ] - extrinsic_L6_7 (traces=2 evals=524) +[ ] - extrinsic_L6_8 (traces=12 evals=12498) +[ ] - extrinsic_L6_9 (traces=11 evals=64005) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 46/94 in 5066.8s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..e5da628a28b338ed69e0ec87f61efd5f66f0a5df --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 44 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s42/train.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/train.log new file mode 100644 index 0000000000000000000000000000000000000000..cdfa3f7f115880436b047875177dde0275a93c24 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s42/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070931-gxouf7is +[2026-06-29T07:09:27.159176] Seeded RNGs with seed=42 +[2026-06-29T07:09:27.159428] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-29T07:09:30.733236] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json + 1405 training examples loaded. + +============================================================ +[2026-06-29T07:09:30.735380] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1405 -> 1405 unique examples + Epoch 1/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 44 total steps, 1405 unique examples (batch_size=64) +[2026-06-29T07:09:40.483509] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:40.490959] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s42/2026-06-29_07-09-27/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 44} diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/summary.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..4b6f41d60e104a66de46643faaeaf7916125175b --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_1_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 44 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt new file mode 100644 index 0000000000000000000000000000000000000000..a31c44eb858251999cf82a3928e0d7d624b42e38 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt @@ -0,0 +1,3 @@ +version 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-> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]).", + "a iff_i", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 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-> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]]]]]; [(not (not x)) -> [[[('P : prop) -> ('Q : prop) 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x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 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x x)]]]])).", + "c em", + "=> (em goal6).", + "c em", + "=> (em x).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]) -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))].", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))])).", + "c em", + "=> (em p@type).", + "a x2", + "=> (and [(not (not x)) -> x] (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))).", + "a and_i", + "=> [(not (not x)) -> x]; (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))])).", + "a x2", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not (not x)) -> x]).", + "a or_e", + "=> [x -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not (not x)) -> x])]; [(not x) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not (not x)) -> x])].", + "a x1", + "=> (and false [x -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not (not x)) -> x])]).", + "a and_i", + "=> false; [x -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [(not (not x)) -> x])].", + "c em", + "=> (em goal15).", + "a not_e", + "=> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))])))); (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))))].", + "a x1", + "=> (and (and x x) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and x x) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and x x) [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (not (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]] -> (and false (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]))]))))])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 473, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> 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(iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e and_i@type x4 and_i).", + "a x2", + "=> (iff (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c em", + "=> (em goal15).", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (iff (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (iff (iff (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 8652, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]].", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]; [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]])].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]])]]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]])]].", + "a or_il", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c em", + "=> (em or_il@type).", + "a or_il", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x2", + "=> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x2", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (or 'P (not 'P))]); [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> (or 'P (not 'P))] -> (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "a x0", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (or 'P (not 'P))])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> (or 'P (not 'P))])].", + "c em", + "=> (em em@type).", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [(or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 381, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "c em", + "=> (em not_i@type).", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)].", + "c em", + "=> (em iff_er@type).", + "intro.", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "a x1", + "=> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]; [(iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])]) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]].", + "c em", + "=> (em p@type@2).", + "a x1", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])])].", + "a x5", + "=> (iff (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (iff (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (iff (iff [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> (or 'P (not 'P))])])]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 33, + "evals_used": 3098, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> [(not (not 'A)) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> [(not (not 'A)) -> 'A]]].", + "intro.", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x0]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x0].", + "intro.", + "c x2", + "=> (x2 or_e@type and_i@type or_e and_i).", + "c x2", + "=> (x2 and_i@type and_i@type x2 x2).", + "c and_el", + "=> (and_el or_e@type and_i@type p0).", + "c x", + "=> (x and_er@type and_i@type and_er x2).", + "c em", + "=> (em x1@type@1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x0]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x0].", + "c x", + "=> (x not_i@type em@type not_i em).", + "c and_el", + "=> (and_el and_i@type and_i@type p1).", + "c x2", + "=> (x2 p1@type or_ir@type p1 or_ir).", + "a p2", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x0]]; [(and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x0]].", + "c and_er", + "=> (and_er and_i@type and_i@type p1).", + "a exfalso" + ] + } + ], + "problem": "extrinsic_L4_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 30287, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 369, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a x2", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "c x1", + "=> (x1 x4).", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not 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-> (iff ['A -> 'B] (or (not 'A) 'B))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]].", + "c em", + "=> (em p7@type).", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]); [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 359, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [[x -> x0] -> (or (not x) x0)]; [(or (not x) x0) -> [x -> x0]].", + "intro.", + "a or_il", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a 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['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and false [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a exfalso", + "=> false.", + "c em", + "=> (em p1@type@2).", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x3", + "=> (x3 and_el@type not_i@type x2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9325, + "actions": [ + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (iff [x -> x0] (or (not x) x0))]; [(not [('P : prop) -> ('Q : prop) -> 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goal15).", + "c x1", + "=> (x1 p9@type x0@type p9).", + "c em", + "=> (em p10@type).", + "c x2", + "=> (x2 p4@type goal12 p4).", + "c x2", + "=> (x2 p0@type p6@type p0).", + "a iff_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 703, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> x]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> x].", + "intro.", + "a x1", + "=> (and x x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and x x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]].", + "c em", + "=> (em goal1).", + "intro.", + "a x2", + "=> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]).", + "c em", + "=> (em goal7).", + "c em", + "=> (em x).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])].", + "a x1", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]).", + "a x1", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])).", + "c em", + "=> (em goal4).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (and (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]))).", + "a and_i", + "=> (and (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])).", + "a x2", + "=> (and (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]) (and (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]))).", + "a and_i", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]); (and (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])).", + "a x1", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]))]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) -> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]))].", + "c em", + "=> (em goal13).", + "intro.", + "a and_i", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) -> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])].", + "a x2", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]]) [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]] -> (and [('P : prop) -> (or 'P (not 'P))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x x)]]]])])]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3382, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> x].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c x1", + "=> (x1 exfalso@type iff_er@type iff_er).", + "c x1", + "=> (x1 and_i@type p@type p).", + "c x1", + "=> (x1 p0@type or_e@type or_e).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p1@type and_er@type and_er).", + "c x1", + "=> (x1 x0@type@1 iff_er@type iff_er).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c x1", + "=> (x1 em@type not_i@type not_i).", + "c em", + "=> (em x0@type).", + "a or_e", + "=> [[x -> (not x)] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a exfalso", + "=> false.", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2612, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e or_e@type x0 or_e).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])] -> false].", + "a x0", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "c em", + "=> (em p@type).", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ['P -> false] -> (not 'P)])); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : 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[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]].", + "c em", + "=> (em goal).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]].", + "intro.", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]].", + "c em", + "=> (em p2@type@2).", + "c x2", + "=> (x2 not_i@type x5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> false] -> [[x -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> 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x", + "=> (x p@type iff_el@type p iff_el).", + "a p2", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c and_er", + "=> (and_er p@type iff_el@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c x", + "=> (x or_ir@type not_i@type or_ir x2).", + "c x", + "=> (x not_i@type iff_el@type not_i p4).", + "a p4", + "=> (iff [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 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exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))).", + "c em", + "=> (em goal0@1).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]].", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "intro.", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em goal9).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "c em", + "=> (em goal1).", + "intro.", + "a 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em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "c em", + "=> (em goal0@2).", + "a not_e", + "=> (not x).", + "a or_e", + "=> [(iff x (not x0)) -> (not x)]; [(not (iff x (not x0))) -> (not x)].", + "intro.", + "c iff_el", + "=> (iff_el x goal0@2@2 x4).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [(iff x (not x0)) -> (not x)]; [(not (iff x (not x0))) -> (not x)].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal3).", + "c em", + "=> (em goal0).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x)); (not x).", + "c em", + "=> (em not_i@type).", + "c p2", + "=> (p2 x2).", + "c not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 404, + "actions": [ + "intro.", 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60, + "evals_used": 3825, + "actions": [ + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [('B : prop) -> (iff (not (iff x 'B)) (iff x (not 'B)))]].", + "a exfalso", + "=> false.", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em goal2).", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> false].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]]; [(not [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))]) -> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> false]].", + "intro.", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] -> [[('A : prop) -> ('B : prop) 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false]; [(not (iff (iff x x1) (and (or x (not x1)) (or (not x) x1)))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5368, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "intro.", + "intro.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a exfalso", + "=> false.", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ['P -> false] -> (not 'P)])); [[false -> ('P : prop) -> 'P] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_ir", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a x1", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a x2", + "=> (or (not 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-> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])].", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : 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prop) -> (and 'P 'Q) -> 'P] -> x1]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])].", + "intro.", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]])] (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> x1]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 44, + "evals_used": 3104, + 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exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "c not_e", + "=> (not_e iff_i@type x4 x3).", + "c em", + "=> (em and_er@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "intro.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em false).", + "a not_e", + "=> (not (not false)); (not false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not (or x [x0 -> x1])); (or x [x0 -> x1]).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not x0); x0.", + "a x5", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))]].", + "a x5", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))]]).", + "c em", + "=> (em goal18).", + "a x5", + "=> (and (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not x0))]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 45, + "evals_used": 78944, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or x [x0 -> x1])); (or x [x0 -> x1]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (not (or x [x0 -> x1]))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> (not (or x [x0 -> x1]))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not (or x [x0 -> x1]))); (not (or x [x0 -> x1])).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> (not (not (or x [x0 -> x1])))]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> (not (not (or x [x0 -> x1])))].", + "intro.", + "a exfalso", + "=> false.", + "c x4", + "=> (x4 and_i@type goal10 iff_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "intro.", + "c x4", + "=> (x4 and_el@type goal1@2 iff_el@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x4", + "=> (x4 p0@type not_i@type goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "intro.", + "c x6" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..0cbede6259fe49b3fff4d0f085fa546bda14c5dd --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,875 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=397) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L0_9 (traces=2 evals=440) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] - extrinsic_L1_1 (traces=2 evals=422) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L2_13 (traces=1 evals=147) +[OK ] g extrinsic_L3_1 (traces=1 evals=27) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L2_6 (traces=3 evals=605) +[OK ] - extrinsic_L3_5 (traces=2 evals=503) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_4 (traces=5 evals=2039) +[OK ] - extrinsic_L1_2 (traces=3 evals=17423) +[OK ] - extrinsic_L1_3 (traces=3 evals=17526) +[OK ] - extrinsic_L0_12 (traces=6 evals=8277) +[OK ] - extrinsic_L3_11 (traces=4 evals=1269) +[OK ] - extrinsic_L3_12 (traces=3 evals=797) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] - extrinsic_L3_14 (traces=3 evals=743) +[OK ] - extrinsic_L3_15 (traces=5 evals=3954) +[OK ] - extrinsic_L3_9 (traces=8 evals=4847) + +thread '' (1467999) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_2 (traces=17 evals=24545) +[OK ] - extrinsic_L3_18 (traces=3 evals=1050) +[OK ] - extrinsic_L3_17 (traces=10 evals=9416) +[ ] - extrinsic_L3_8 (traces=17 evals=28948) +[ ] - extrinsic_L3_7 (traces=13 evals=25861) +[OK ] - extrinsic_L3_16 (traces=8 evals=20525) +[ ] - extrinsic_L3_10 (traces=13 evals=22870) +[OK ] - extrinsic_L3_23 (traces=8 evals=6413) +[ ] - extrinsic_L3_19 (traces=17 evals=21045) + +thread '' (1467999) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_21 (traces=17 evals=22407) +[ ] - extrinsic_L3_20 (traces=17 evals=26373) +[ ] - extrinsic_L3_22 (traces=17 evals=27135) +[ ] - extrinsic_L3_24 (traces=17 evals=27210) + +thread '' (1467999) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L3_25 (traces=16 evals=33715) +[ ] - extrinsic_L3_26 (traces=11 evals=10943) +[ ] - extrinsic_L4_1 (traces=17 evals=17432) +[ ] - extrinsic_L3_27 (traces=10 evals=19496) +[ ] - extrinsic_L3_29 (traces=17 evals=24737) +[ ] - extrinsic_L3_28 (traces=13 evals=24830) +[OK ] - extrinsic_L4_4 (traces=7 evals=14817) +[OK ] - extrinsic_L4_6 (traces=7 evals=15033) + +thread '' (1468003) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_2 (traces=13 evals=20169) +[ ] - extrinsic_L4_3 (traces=17 evals=30287) +[OK ] - extrinsic_L4_5 (traces=7 evals=39213) + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_7 (traces=14 evals=33725) +[ ] - extrinsic_L4_9 (traces=17 evals=20103) +[ ] - extrinsic_L4_8 (traces=15 evals=23686) +[ ] - extrinsic_L4_10 (traces=11 evals=35475) +[ ] - extrinsic_L4_11 (traces=11 evals=22204) +[ ] - extrinsic_L4_12 (traces=13 evals=29973) + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_14 (traces=10 evals=25249) +[ ] - extrinsic_L4_13 (traces=13 evals=14338) + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_1 (traces=3 evals=16653) + +thread '' (1467999) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468005) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_2 (traces=13 evals=29008) + +thread '' (1468002) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L5_3 (traces=17 evals=26066) + +thread '' (1468002) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468002) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L5_4 (traces=12 evals=24147) + +thread '' (1468004) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1467999) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_5 (traces=17 evals=27446) +[ ] - extrinsic_L5_6 (traces=11 evals=12392) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_7 (traces=17 evals=29847) + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=16 evals=20893) + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468006) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=17 evals=33275) +[ ] - extrinsic_L5_10 (traces=6 evals=20965) +[OK ] g extrinsic_L6_6 (traces=1 evals=61) +[ ] - extrinsic_L5_11 (traces=15 evals=60100) +[ ] - extrinsic_L6_2 (traces=13 evals=9893) +[ ] - extrinsic_L6_3 (traces=10 evals=11730) +[ ] - extrinsic_L6_5 (traces=2 evals=102052) +[ ] - extrinsic_L6_7 (traces=4 evals=1669) +[ ] - extrinsic_L6_9 (traces=5 evals=80919) +[ ] - extrinsic_L6_4 (traces=3 evals=206863) +[ ] - extrinsic_L6_8 (traces=3 evals=167869) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 52/94 in 5581.7s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..e5da628a28b338ed69e0ec87f61efd5f66f0a5df --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 44 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s43/train.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/train.log new file mode 100644 index 0000000000000000000000000000000000000000..a5fc599a85387af24c2ab9bdc9de42a1125375e6 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s43/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070947-epszdd03 +[2026-06-29T07:09:43.722508] Seeded RNGs with seed=43 +[2026-06-29T07:09:43.722766] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-29T07:09:47.159380] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json + 1405 training examples loaded. + +============================================================ +[2026-06-29T07:09:47.161505] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1405 -> 1405 unique examples + Epoch 1/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 44 total steps, 1405 unique examples (batch_size=64) +[2026-06-29T07:09:57.043553] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:57.051590] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s43/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 44} diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/summary.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..20013ee50efe1e29a0c64b8d2db75c89b8aec356 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_1_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 44 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt new file mode 100644 index 0000000000000000000000000000000000000000..97cc40ff7873b0dc31c88f55c31cb3a1783b92ce --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5c3c96779262ccf8addcca301fc07284a7f42835d022c571efa9c2e0b2bde1a9 +size 318254491 diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/ablation_config.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/ablation_config.json new file mode 100644 index 0000000000000000000000000000000000000000..4dfd41be247ae5753dd6fa78d2dbb48037f7b0c6 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/ablation_config.json @@ -0,0 +1,8 @@ +{ + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1, + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json" +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt new file mode 100644 index 0000000000000000000000000000000000000000..a1c242dee58199b3325ee52be4c6ec1e2873e805 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:96514e1b98002c9d9eb75fdd9dcd53432b2c3098c40cac0714ec886bb20524de +size 318283327 diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_2.pt b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_2.pt new file mode 100644 index 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(or false (not false))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]] false).", + "a x2", + "=> (and false (and [(not (or false (not false))) -> [[('P : prop) -> (or 'P (not 'P))] -> false]] false))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 583, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em not_e@type).", + "intro.", + "a or_il", + "=> x0.", + "a or_e", + "=> [x -> x0]; [x0 -> x0].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [x0 -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]]; [x0 -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]].", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]]].", + "intro.", + "c em", + "=> (em goal).", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]]]; [(not false) -> [x -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [x -> false]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal13).", + "a x3", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x4", + "=> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]).", + "a or_e", + "=> [(or false (not false)) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]; [(not (or false (not false))) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> [(or false (not false)) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> [(or false (not false)) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]].", + "a x4", + "=> (and (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> [(or false (not false)) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]).", + "c em", + "=> (em goal20).", + "a x4", + "=> (and (or [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] (not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)])) (and (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> [(or false (not false)) -> (and (not false) [[('P : prop) -> (not 'P) -> 'P -> false] -> false])]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7630, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "c x", + "=> (x or_e@type goal1 or_e).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "c x", + "=> (x p@type exfalso@type p).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) -> false]; [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em", + "=> (em goal).", + "c x", + "=> (x and_el@type or_ir@type and_el).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x", + "=> (x and_el@type goal6 and_el).", + "a exfalso", + "=> false.", + "c em", + "=> (em p3@type).", + "c x", + "=> (x p3@type goal8 p3).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] -> false]; [(not [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)]) -> false].", + "intro.", + "c x2", + "=> (x2 goal p2@type@2 p2).", + "c em", + "=> (em or_ir@type).", + "c x", + "=> (x or_e@type p5@type or_e).", + "a x1", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])])); [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]) -> false]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]) -> false].", + "a x", + "=> .", + "intro.", + "c x", + "=> (x or_ir@type and_el@type or_ir).", + "a x1", + "=> (or (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [false -> ('P : prop) -> 'P]) -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 421, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or x x0) -> (or x0 x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or x x0) -> (or x0 x)]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or x x0) -> (or x0 x)]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or x x0) -> (or x0 x)]]].", + "intro.", + "a x1", + "=> (iff [(or x x0) -> (or x0 x)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not x)].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not x)]].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [false -> ('P : prop) -> 'P])].", + "a x1", + "=> (iff (not [false -> ('P : prop) -> 'P]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal).", + "c em", + "=> (em p2@type).", + "a iff_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [false -> ('P : prop) -> 'P])].", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [false -> ('P : prop) -> 'P])).", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + 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prop) -> ['P -> false] -> (not 'P)]) -> [('B : prop) -> (or x 'B) -> (or 'B x)]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (or x 'B) -> (or 'B x)]]]].", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a x1", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x3", + "=> (x3 p@type@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]].", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c x3", + "=> (x3 goal0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em p@type).", + "c x3", + "=> (x3 goal19).", + "intro.", + "c em", + "=> (em goal13).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em p5@type).", + "a or_e", + "=> [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3284, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q 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prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 iff_el).", + "a x", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] -> false])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]) [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P 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-> (and (not x0) [false -> ('P : prop) -> 'P])] -> (not [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> false]]) (not [('P : prop) -> (or 'P (not 'P))])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not x0) [false -> ('P : prop) -> 'P])] -> (not [('P : prop) -> (or 'P (not 'P))])]]]).", + "a x6", + "=> (and (and (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not x0) [false -> ('P : prop) -> 'P])] -> (not [('P : prop) -> (or 'P (not 'P))])]] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x0 -> false]]) (not [('P : prop) -> (or 'P (not 'P))])) [[('P : prop) -> ('Q : prop) -> (and 'P 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prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "c em", + "=> (em goal).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false])).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]))]; [(not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]) -> (and [[('P : prop) -> ('Q : prop) -> ('R 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['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]))].", + "a or_e", + "=> [(and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]))]; [(not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (not [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]))].", + "a exfalso", + "=> false.", + "a x", + "=> (or (or (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))) [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]))]); [(or (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))) -> false]; [[[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> (not 'P) -> 'P -> false]))] -> false].", + "a or_il", + "=> .", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> 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prop) -> 'P -> 'Q -> (and 'P 'Q)]))] false)].", + "a x", + "=> (or (not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)) [('P : prop) -> (not 'P) -> 'P -> false]); [(not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false)) -> (or (and [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (or (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))))]; [[('P : prop) -> (not 'P) -> 'P -> false] -> (or (and [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (or (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false) (not (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) false))))].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] false).", + "c x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 432, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(and (not x) (not x0)) -> (not (or x x0))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]].", + "intro.", + "a x1", + "=> (iff [(and (not x) (not x0)) -> (not (or x x0))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]]) -> false].", + "a x1", + "=> (iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]]).", + "c x2", + "=> (x2 iff_er).", + "c p2", + "=> (p2 x1).", + "c em", + "=> (em goal6).", + "c p2", + "=> (p2 iff_er).", + "c x2", + "=> (x2 x1).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not x) (not x0)) -> (not (or x x0))]]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])])); (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]))].", + "c em", + "=> (em goal14)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4148, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x", + "=> (or [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))]); [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false]; [[('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] -> false].", + "a or_ir", + "=> [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))].", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (or 'P (not 'P))]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c em", + "=> (em not_e@type).", + "a or_ir", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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false]].", + "c em", + "=> (em p2@type).", + "c em", + "=> (em goal0@1@2).", + "a or_e", + "=> [(or [x -> [x0 -> x]] (not [x -> [x0 -> x]])) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not (or [x -> [x0 -> x]] (not [x -> [x0 -> x]]))) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "c em", + "=> (em goal0@1).", + "a or_e", + "=> [[x -> [x0 -> x]] -> false]; [(not [x -> [x0 -> x]]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [x0 -> false].", + "c em", + "=> (em p2@type@2).", + "a or_e", + "=> [(or [x -> [x0 -> x]] (not [x -> [x0 -> x]])) -> [x -> false]]; [(not (or [x -> [x0 -> x]] (not [x -> [x0 -> x]]))) -> [x -> false]].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] -> [(or [x -> [x0 -> x]] (not [x -> [x0 -> x]])) -> [x -> false]]]; [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)]) -> [(or [x -> [x0 -> x]] (not [x -> [x0 -> x]])) -> [x -> false]]].", + "c em", + "=> (em p6@type).", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[x -> [x0 -> x]] -> false]); [[x -> [x0 -> x]] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6889, + "actions": [ + "c em", + "=> (em or_ir@type).", + "intro.", + "intro.", + "a iff_i", + "=> [(and x (or x x0)) -> x]; [x -> (and x (or x x0))].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> x].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "c x3", + "=> (x3 em@type goal0@1 x1).", + "c x3", + "=> (x3 goal and_er@type and_er).", + "c x2", + "=> (x2 p@type@2 or_ir@type x3).", + "c x2", + "=> (x2 iff_i@type or_ir@type x2).", + "c x3", + "=> (x3 not_e@type not_i@type not_i)." + ] + } + ], + "problem": "extrinsic_L3_16" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 20902, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 363, + "actions": [ + "intro.", + "intro.", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "a not_e", + "=> .", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "a not_e", + "=> (not (not 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]].", + "c em", + "=> (em goal11).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]] -> 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-> 'R] -> 'R])]]] -> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]]]) -> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])].", + "intro.", + "c x1", + "=> (x1 and_i).", + "a not_i", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false].", + "intro.", + "a not_e", + "=> (not (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)])); (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]).", + "c em", + "=> (em goal16).", + "a not_i", + "=> [(not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6798, + "actions": [ + "intro.", + 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em p3@type).", + "c em", + "=> (em false).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em p7@type@2).", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "c em", + "=> (em x0@type@1@1).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> (or 'P (not 'P))]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "c em", + "=> (em goal6).", + "a x2", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]); [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] -> false].", + "a x2", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2229, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em exfalso@type).", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "c x2", + "=> (x2 exfalso@type or_ir@type exfalso or_ir).", + "c x2", + "=> (x2 or_ir@type iff_el@type or_ir iff_el).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 and_el@type not_i@type and_el not_i).", + "a not_e", + "=> (not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c and_el", + "=> (and_el and_el@type not_i@type p2).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el exfalso@type or_ir@type p0).", + "c and_el", + "=> (and_el or_ir@type iff_el@type p1).", + "a not_e", + "=> (not (not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)]))); (not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c p5", + "=> (p5 and_er@type em@type em).", + "a p4", + "=> false.", + "c em", + "=> (em goal).", + "a x1", + "=> false.", + "c p3", + "=> (p3 and_el@type not_i@type p2).", + "a exfalso", + "=> false.", + "a p8", + "=> (and false (not (not (not x)))).", + "c em", + "=> (em goal15).", + "c em", + "=> (em or_e@type).", + "a p8", + "=> (and (and false (not (not (not x)))) (not (not (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> ['P -> false] -> (not 'P)])))).", + "c p3", + "=> (p3 exfalso@type or_ir@type p0).", + "c p8", + "=> (p8 exfalso@type or_ir@type p0)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 510, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (not (not (not 'A))) -> (not 'A)]); [('A : prop) -> (not (not (not 'A))) -> (not 'A)].", + "a not_i", + "=> [[('A : prop) -> (not (not (not 'A))) -> (not 'A)] -> false].", + "intro.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x0", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a and_i", + "=> false.", + "a x0", + "=> 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'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a x1", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x2", + "=> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] false).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]].", + "a x1", + "=> (iff false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x2", + "=> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [false -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "c x3", + "=> (x3 x1).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 606, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a and_i", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "a and_i", + "=> false.", + "c em", + "=> (em iff_i@type).", + "a x0", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and [false -> ('P : prop) -> 'P] (and false [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a and_i", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])] (and false [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c em", + "=> (em false).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]; (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])).", + "c em", + "=> (em goal9).", + "a and_i", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "c em", + "=> (em goal).", + "a x0", + "=> (and (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]) [('P : prop) -> (or 'P (not 'P))]).", + "a and_i", + "=> (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]).", + "a x", + "=> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]))].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) (and [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (and false [('P : prop) -> ['P -> false] -> (not 'P)])]))] (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 8129, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em em@type).", + "c em", + "=> (em and_el@type).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]].", + "intro.", + "a x0", + "=> (and [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]).", + "a x0", + "=> (and (and [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false] [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "a x", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])]; [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> (not 'P) -> 'P -> false])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a x", + "=> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]); [(or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x", + "=> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); [(not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (or (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "intro.", + "c x1", + "=> (x1 and_i@type iff_er@type and_i iff_er).", + "c and_el", + "=> (and_el and_i@type iff_er@type p2).", + "c p3", + 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> false]].", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or false (not false)) -> false]; [(not (or false (not false))) -> false].", + "intro.", + "c em", + "=> (em p4@type).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em not_e@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 539, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> 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or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]]; [(not [('A : prop) -> (iff 'A (not 'A)) -> false]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> false]].", + "a exfalso", + "=> false.", + "a x1", + "=> (not (or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])))].", + "intro.", + "a not_i", + "=> [(or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])) -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [(or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])) -> false]].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em goal13).", + "a or_e", + "=> [false -> [(or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])) -> false]]; [(not false) -> [(or [('A : prop) -> (iff 'A (not 'A)) -> false] (not [('A : prop) -> (iff 'A (not 'A)) -> false])) -> false]].", + "c em", + "=> (em x0@type@2).", + "intro.", + "c em", + "=> (em goal16).", + "a exfalso", + "=> .", + "c em", + "=> (em p4@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "dead", + "depth_used": 45, + "evals_used": 1975, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : 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(not x)) -> false]; [(not (iff x (not x))) -> false].", + "c iff_er", + "=> (iff_er x x0@type@2 x3).", + "c x1", + "=> (x1 iff_el@type x5 iff_el).", + "c not_e", + "=> (not_e iff_el@type x5 iff_el).", + "intro.", + "c em", + "=> (em p0@type).", + "c em", + "=> (em and_el@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 846, + "actions": [ + "intro.", + "intro.", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "intro.", + "a x1", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] false).", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> (not 'P) -> 'P -> false] false)).", + "c em", + "=> (em goal4).", + "c em", + "=> (em or_il@type).", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [(and [('P : prop) -> (not 'P) -> 'P -> false] false) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not (and [('P : prop) -> (not 'P) -> 'P -> false] false)) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(and [('P : prop) -> (not 'P) -> 'P -> false] false) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(and [('P : prop) -> (not 'P) -> 'P -> false] false) -> (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]].", + "intro.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(and [('P : prop) -> (not 'P) -> 'P -> false] false) -> 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(not 'A)) -> false] (iff x (not x))); [[('A : prop) -> (iff 'A (not 'A)) -> false] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [x -> false]]]; [(iff x (not x)) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [x -> false]]].", + "c x2", + "=> (x2 p@type and_er@type and_er).", + "a or_ir", + "=> .", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(not x) -> x]).", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 577, + "actions": [ + "intro.", + "c em", + "=> (em false).", + "intro.", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "a or_e", + "=> [false -> (not false)]; [(not false) -> (not false)].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [false -> false]; [(not false) -> false].", + "intro.", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_i@type).", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x)); (not x).", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em goal1).", + "c em", + "=> (em p4@type@2).", + "c em", + "=> (em p8@type@2).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "intro.", + "a not_e", + "=> (not (or false (not false))).", + "c em", + "=> (em p9@type@2).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or false (not false)))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (or false (not false)))].", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 52, + "evals_used": 2630, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "a x0", + "=> (or [false -> ('P : prop) -> 'P] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]); [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_il", + "=> .", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a x0", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [[[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a or_ir", + "=> [[false -> ('P : prop) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a exfalso", + "=> false.", + "a x0", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false); [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [false -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)].", + "a x1", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)])].", + "a x0", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) false)])]]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 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-> [x -> [x -> (not (not x))]]] (and (not (not x)) (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (iff x (not (not x))) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) false)))))]).", + "c em", + "=> (em and_er@type).", + "a x0", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and [('P : prop) -> (or 'P (not 'P))] [x -> [x -> (not (not x))]])); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [x -> (not (not x))]]] (and (not (not x)) (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (iff x (not (not x))) (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) false)))))].", + "a x0", + "=> (and [('P : prop) -> (or 'P (not 'P))] [x -> [x -> (not (not x))]]).", + "c and_el", + "=> (and_el iff_el@type p@type 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-> (not 'P)] -> [x -> (not (not x))]] -> [x -> (not (not x))]]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [x -> (not (not x))]]) -> [x -> (not (not x))]].", + "c em", + "=> (em iff_i@type).", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 11361, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q 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: prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "a x", + "=> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em goal12).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "intro.", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "a or_il", + "=> .", + "a x1", + "=> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))); [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "c em", + "=> (em goal18).", + "a x", + "=> (or [false -> ('P : prop) -> 'P] (or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))); [[false -> ('P : prop) -> 'P] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(or (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c em", + "=> (em goal20).", + "a x", + "=> (or (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]) [('P : prop) -> ['P -> false] -> (not 'P)]); [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : 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'Q]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p3@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x1", + "=> (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x2", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a x1", + "=> (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a iff_i", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a x1", + "=> (iff (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x2", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "a x1", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 513, + "actions": [ + "c em", + "=> (em not_i@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (not x)) -> x]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]]].", + "intro.", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not (not x)) -> x]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [(not (not x)) -> x]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em x).", + "intro.", + "c em", + "=> (em false).", + "a x3", + "=> (and false (not x)).", + "c em", + "=> (em goal3).", + "a and_i", + "=> false; (not x).", + "c em", + "=> (em p@type@2).", + "a x5", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> false; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a x3", + "=> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [x -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not x) -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a x5", + "=> (and [x -> (and false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])] (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 6759, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a not_e", + "=> (not [('A : prop) -> [(not (not 'A)) -> 'A]]); [('A : prop) -> [(not (not 'A)) -> 'A]].", + "c x", + "=> (x not_e@type iff_i@type not_e).", + "c em", + "=> (em and_el@type).", + "a not_i", + "=> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false]].", + "intro.", + "c x0", + "=> (x0 and_el@type iff_el@type and_el iff_el).", + "c x", + "=> (x p@type and_i@type p).", + "c and_er", + "=> (and_er and_el@type iff_el@type p2).", + "c x0", + "=> (x0 iff_el@type iff_el@type iff_el p4).", + "c x0", + "=> (x0 em@type p5@type em p5).", + "c x", + "=> (x p3@type p0@type p3).", + "c x0", + "=> (x0 or_il@type and_i@type or_il x0).", + "c x", + "=> (x and_i@type p7@type and_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false]]; [(or (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (or [('P : prop) -> (not 'P) -> 'P -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false]].", + "c and_el", + "=> (and_el or_il@type and_i@type p8).", + "intro.", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "c and_el", + "=> (and_el iff_el@type iff_el@type p5).", + "a p11", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] false).", + "c x2", + "=> (x2 p0@type).", + "c x2", + "=> (x2 p8@type).", + "c p10", + "=> (p10 p7@type goal14 p7).", + "c x0", + "=> (x0 not_i@type iff_el@type not_i p11)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 650, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> (or 'P (not 'P))] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> (or 'P (not 'P))] -> false]]].", + "intro.", + "intro.", + "a x1", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])]).", + "a x2", + "=> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])).", + "c em", + "=> (em not_e@type).", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])]).", + "a x2", + "=> (and x (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])).", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type@2).", + "a exfalso", + "=> false.", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a and_i", + "=> false.", + "a x1", + "=> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])] (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false)).", + "a and_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])]; (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false).", + "a x2", + "=> (and (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])]).", + "a and_i", + "=> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false)].", + "a x2", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [[('P : prop) -> (or 'P (not 'P))] -> false])])) false)]).", + "c em", + "=> (em em@type).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 480, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> [(not (not 'A)) -> 'A]]); [('A : prop) -> [(not (not 'A)) -> 'A]].", + "a not_i", + "=> [[('A : prop) -> [(not (not 'A)) -> 'A]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", 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-> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_e", + "=> [[(not x) -> x0] -> [[false -> ('P : prop) -> 'P] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]]; [(not [(not x) -> x0]) -> [[false -> ('P : prop) -> 'P] -> (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]].", + "c x4", + "=> (x4 p2@type p5@type p2 p5).", + "c and_el", + "=> (and_el p0@type iff_i@type p3).", + "c and_el", + "=> (and_el not_e@type p0@type p5).", + "a exfalso", + "=> false.", + "c x4" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 696, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a x0", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false).", + "a x", + "=> (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal7).", + "a and_i", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false).", + "a and_i", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); false.", + "c em", + "=> (em or_il@type).", + "a x", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false] (or (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) (not (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false)))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> (or 'P (not 'P))]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]).", + "c em", + "=> (em or_e@type).", + "a and_i", + "=> false; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "a x0", + "=> (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x0", + "=> (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])).", + "a x", + "=> (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x", + "=> (and (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x0", + "=> (and (and (and (and (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (and false (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 301, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> x]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> x].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> x]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> x].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> x]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> x].", + "c em", + "=> (em not_i@type).", + "a x3", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x)]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x)].", + "a x3", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x)).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x))].", + "a x3", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x))).", + "a iff_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x))]; [(iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] x)) -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "a x4", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ['P -> false] -> (not 'P)] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x4", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4885, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]]].", + "intro.", + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "intro.", + "c x", + "=> (x and_el@type not_e@type and_el not_e).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [false -> ('P : prop) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em em@type).", + "intro.", + "c and_el", + "=> (and_el and_el@type not_e@type p0).", + "a p3", + "=> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "c x", + "=> (x and_i@type em@type x4 em).", + "a or_e", + "=> [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [(not x1) -> x0]) -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a p3", + "=> (and [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))] [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))] [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))])]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))] [[(not x1) -> x0] -> (and (not [false -> ('P : prop) -> 'P]) (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))])].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal10).", + "c and_el", + "=> (and_el and_i@type em@type p4).", + "c em", + "=> (em x0).", + "a not_e", + "=> (not [(not x0) -> x1]).", + "a not_i", + "=> [[(not x0) -> x1] -> false].", + "c x4", + "=> (x4 p1@type x3@type p1 x3).", + "c em", + "=> (em p5@type@2).", + "c x", + "=> (x p8@type iff_er@type p8 iff_er).", + "c x5", + "=> (x5 p8@type and_i@type p8 and_i).", + "c p6", + "=> (p6 p4@type and_el@type p4 and_el).", + "c and_el" + ] + 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em", + "=> (em iff_el@type).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "intro.", + "c x0", + "=> (x0 and_el@type or_il@type x or_il).", + "c x", + "=> (x and_el@type or_il@type p2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a p3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]).", + "a p3", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a p3", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c x0", + "=> (x0 and_i@type iff_er@type and_i iff_er).", + "c em", + "=> (em em@type).", + "c and_er", + "=> (and_er and_i@type iff_er@type p4).", + "c and_el", + "=> (and_el and_el@type or_il@type p2).", + "c em", + "=> (em p5@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c p7", + "=> (p7 and_el@type or_il@type p2).", + "c p9", + "=> (p9 and_el@type or_il@type p2).", + "c p10", + "=> (p10 and_el@type or_il@type p2).", + "c p9", + "=> (p9 and_i@type iff_er@type p4).", + "a p7", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7082, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [[x -> x0] -> (or (not x) x0)]; [(or (not x) x0) -> [x -> x0]].", + "intro.", + "a or_ir", + "=> x0.", + "a x1", + "=> x.", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]); [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c em", + "=> (em or_ir@type).", + "c x2", + "=> (x2 goal0@2 em@type).", + "c iff_el", + "=> (iff_el p1@type@1 p1@type@2 p1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]).", + "c em", + "=> (em p0@type).", + "c em", + "=> (em goal).", + "c iff_er", + "=> (iff_er p1@type@1 p1@type@2 p1).", + "c x2", + "=> (x2 goal goal0@2).", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false].", + "c x2", + "=> (x2 and_i@type p4@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]].", + "c em", + "=> (em p0@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]]].", + "c iff_el", + "=> (iff_el p7@type@1 p7@type@2 p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]]]].", + "c iff_el", + "=> (iff_el p6@type@1 p6@type@2 p6).", + "intro.", + "c x2", + "=> (x2 p7@type@2@1 p0@type@2).", + "c iff_el", + "=> (iff_el p11@type@1 p11@type@2 p11).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 539, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [[x -> x0] -> (or (not x) x0)]; [(or (not x) x0) -> [x -> x0]].", + "intro.", + "a or_ir", + "=> x0.", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> x0]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> x0].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> x0]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> x0]].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "a x2", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal0).", + "a iff_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "c em", + "=> (em exfalso@type).", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])).", + "c em", + "=> (em goal1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]].", + "c em", + "=> (em x0).", + "a x2", + "=> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em p3@type@2).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])]; [(not [false -> ('P : prop) -> 'P]) -> (iff (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] -> false]; [(not [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 696, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])].", + "intro.", + "c em", + "=> (em or_ir@type).", + "a x0", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a x", + "=> (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "c em", + "=> (em goal7).", + "a and_i", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a and_i", + "=> (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_il@type).", + "a x", + "=> (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false] (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> false.", + "a x", + "=> (and false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "c em", + "=> (em or_e@type).", + "a and_i", + "=> false.", + "a x0", + "=> (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a x0", + "=> (and (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x", + "=> (and (and (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])).", + "a x", + "=> (and (and (and (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x0", + "=> (and (and (and (and (and false (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and false (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 291, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [[x -> x0] -> (or (not x) x0)]; [(or (not x) x0) -> [x -> x0]].", + "intro.", + "a or_ir", + "=> x0.", + "a x1", + "=> x.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (not x) x0)); (or (not x) x0).", + "a not_i", + "=> [(or (not x) x0) -> false].", + "intro.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [(not x) -> (not false)]; [x0 -> (not false)].", + "a or_e", + "=> [(not x) -> [(not x) -> (not false)]]; [x0 -> [(not x) -> (not false)]].", + "intro.", + "a or_e", + "=> [(not x) -> [(not x) -> (not false)]]; [x0 -> [(not x) -> (not false)]].", + "intro.", + "a or_e", + "=> [(not x) -> [(not x) -> (not false)]]; [x0 -> [(not x) -> (not false)]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not x) -> false]; [x0 -> false].", + "intro.", + "a or_e", + "=> [(not x) -> false]; [x0 -> false].", + "a or_e", + "=> [(not x) -> [(not x) -> false]]; [x0 -> [(not x) -> false]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not x) -> false]; [x0 -> false].", + "intro.", + "c em", + "=> (em goal0@2).", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not x) -> false]; [x0 -> false].", + "intro.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [(or (not x) x0) -> (not (not false))]; [(not (or (not x) x0)) -> (not (not false))].", + "c em", + "=> (em and_el@type).", + "intro.", + "a not_i", + "=> [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 57, + "evals_used": 4436, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B 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-> (or 'A ['A -> 'B])] -> false].", + "c em", + "=> (em goal8).", + "a exfalso", + "=> false.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]); [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x1", + "=> (x1 exfalso@type exfalso@type).", + "c x1", + "=> (x1 or_e@type goal3).", + "a exfalso", + "=> false.", + "c em", + "=> (em p7@type).", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 p4@type@2 p8@type).", + "c x1", + "=> (x1 p2@type p4@type@2).", + "a not_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 506, + "actions": [ + "intro.", + "intro.", + 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prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])].", + "c em", + "=> (em p@type).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]]; [(not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not 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('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]).", + "a or_e", + "=> [(or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))) -> (and [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]; [(not (or (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))))) -> (and [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) -> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])] [[('P : prop) -> ['P -> false] -> (not 'P)] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 457, + "actions": [ + "intro.", + "intro.", + "a or_ir", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x0]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> x0].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x0]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> x0].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 696, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [('P : prop) -> ('Q 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"a and_i", + "=> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em or_il@type).", + "a x", + "=> (and (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a and_i", + "=> false.", + "a x", + "=> (and false [('P : prop) -> (not 'P) -> 'P -> false]).", + "c em", + "=> (em not_i@type).", + "a and_i", + "=> false.", + "a x0", + "=> (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x0", + "=> (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a x0", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1957, + "actions": [ + "intro.", + "intro.", + "a or_ir", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> false.", + "a x2", + "=> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])].", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])])] x0).", + "a exfalso", + "=> false.", + "a x2", + "=> (and false false).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and false false)]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (and false false)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and false false)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and false false)]].", + "c em", + "=> (em goal13).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em x0).", + "c x3", + "=> (x3 and_er@type p@type and_er).", + "c x4", + "=> (x4 p0@type p3@type p0).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": 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"=> (em or_e@type).", + "a or_e", + "=> [[x0 -> x1] -> x1]; [(not [x0 -> x1]) -> x1].", + "c x3", + "=> (x3 iff_er@type p@type iff_er p).", + "c and_er", + "=> (and_er iff_er@type p@type p9).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el iff_er@type p@type p9).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "c and_el", + "=> (and_el p1@type p5@type p7).", + "c x", + "=> (x p4@type and_er@type p4 and_er).", + "c em", + "=> (em p8@type@2).", + "c em" + ] + } + ], + "problem": "extrinsic_L4_10" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 13, + "evals_used": 50685, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 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or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a x1", + "=> false.", + "a x3", + "=> false.", + "a not_e", + "=> (not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))).", + "a x4", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a x4", + "=> false.", + "a x2", + "=> false.", + "a x4", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a x", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]].", + "c em", + "=> (em goal7).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "c em", + "=> (em goal1).", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] false).", + "c em", + "=> (em goal6).", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] false)]; [(not (not [false -> ('P : prop) -> 'P])) -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] false)].", + "intro.", + "a x", + "=> false.", + "c not_e", + "=> (not_e exfalso@type x1 x).", + "a exfalso", + "=> false.", + "a x", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]) -> false].", + "intro.", + "c x1", + "=> (x1 x0).", + "a x", + "=> false.", + "a x0", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])) false).", + "a x0", + "=> (and (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]) (and (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])])) false)).", + "a x", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]]) -> false].", + "a or_e", + "=> [(not [false -> ('P : prop) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]]; [(not (not [false -> ('P : prop) -> 'P])) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]] -> false]].", + "c em", + "=> (em goal22)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 495, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "intro.", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a not_e", + "=> [x -> (not x)].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [x -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [x -> (not x)]].", + "intro.", + "a x1", + "=> (iff (not x) x).", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em or_ir@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x1", + "=> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p5@type).", + "a iff_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a x2", + "=> (iff (not [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "a x1", + "=> (iff false (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))." + ] + }, + { + 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false.", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c x0", + "=> (x0 not_i).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]].", + "intro.", + "c x0", + "=> (x0 x1).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal12).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]] -> false]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]]]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a x1", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1486, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c em", + "=> (em and_i@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))].", + "a x0", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))]).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))])).", + "c em", + "=> (em goal12).", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))]))).", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (not [('P : 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'P 'Q) -> 'Q]) (and (not [('P : prop) -> (not 'P) -> 'P -> false]) false))])).", + "c x1", + "=> (x1 or_il@type or_ir@type or_il or_ir).", + "c x0", + "=> (x0 and_i@type em@type p3).", + "c em", + "=> (em p3@type).", + "c x0", + "=> (x0 or_il@type or_ir@type p4).", + "a x0", + "=> (and (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c p5", + "=> (p5 goal15).", + "c p5", + "=> (p5 goal11).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 602, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em or_ir@type).", + "a x1", + "=> (and [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q 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prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]].", + "c em", + "=> (em goal10).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [x -> false]; [(not x) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> false]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [x -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> false]]].", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [(or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]])) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))]; [(not (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]] (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]])]]]))) -> (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))].", + "intro.", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": 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p6@type).", + "c x1", + "=> (x1 or_e@type).", + "c x1", + "=> (x1 p6@type@2).", + "c x1", + "=> (x1 p@type).", + "intro.", + "c x1", + "=> (x1 p8@type).", + "a or_e", + "=> [(or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P])) -> [[false -> ('P : prop) -> 'P] -> [[(not x) -> x] -> false]]]; [(not (or [false -> ('P : prop) -> 'P] (not [false -> ('P : prop) -> 'P]))) -> [[false -> ('P : prop) -> 'P] -> [[(not x) -> x] -> false]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> false]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> false].", + "c em", + "=> (em and_i@type).", + "c x1", + "=> (x1 and_i@type).", + "c x1", + "=> (x1 goal8).", + "c x2", + "=> (x2 x0).", + "c x1", + "=> (x1 or_ir@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4240, + "actions": [ + "intro.", + "intro.", + "a x0", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_il@type).", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "c x2", + "=> (x2 not_e@type and_el@type not_e).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "c x2", + "=> (x2 iff_i@type iff_el@type iff_i).", + "c x2", + "=> (x2 or_e@type not_e@type or_e).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 and_er@type goal2 and_er).", + "a not_e", + "=> (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]); [('A : prop) -> [(not 'A) -> 'A] -> 'A].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q 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-> 'P] -> (iff 'P 'Q)])].", + "intro.", + "c x2", + "=> (x2 or_il@type x0@type x2).", + "c em", + "=> (em p@type).", + "c em", + "=> (em p1@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not [false -> ('P : prop) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [[(not x) -> x] -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "intro.", + "a x3", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "c x4", + "=> (x4 not_i@type x not_i).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 iff_er@type p3@type iff_er).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [(not x) -> x]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [(not x) -> x]))) -> false].", + "a x3", + "=> false.", + "c x2", + "=> (x2 and_er@type p5@type and_er).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (or (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [(not x) -> x]) (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] [(not x) -> x])))) -> false].", + "c x4", + "=> (x4 exfalso@type p1@type exfalso).", + "c x4", + "=> (x4 exfalso@type goal13 x3).", + "a x3", + "=> false.", + "a x3", + "=> false.", + "c x4", + "=> (x4 or_ir@type goal5 or_ir)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 1595, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "c em", + "=> (em goal).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('A : prop) -> [(not 'A) -> 'A] -> 'A]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "c x0", + "=> (x0 exfalso@type and_er@type and_er).", + "a x2", + "=> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> [(not [[('P 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]].", + "c em", + "=> (em or_e@type).", + "a x2", + "=> [(not [(not [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]) -> [(not [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [(not [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) 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'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]) -> [(not [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]]].", + "c em", + "=> (em goal17).", + "c x0", + "=> (x0 goal16 or_il@type or_il).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [(not [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]) -> [[false -> ('P : prop) -> 'P] -> [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) 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prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and x (or (not x) x0)) -> (and x x0)]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "c em", + "=> (em goal0@1@2).", + "c em", + "=> (em p4@type@2).", + "a iff_i", + "=> [(iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and x (or (not x) x0)) -> (and x x0)]]) -> [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and x (or (not x) x0)) -> (and x x0)]])].", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (iff false [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and x (or (not x) x0)) -> (and x x0)]])).", + "c em", + "=> (em p3@type@2).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a 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-> (not 'P)])))]]; [[[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))] -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "intro.", + "a x2", + "=> (iff [('P : prop) -> ['P -> false] -> (not 'P)] (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))).", + "a iff_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> [('P : prop) -> ['P -> false] -> (not 'P)]].", + "a exfalso", + "=> false.", + "a x0", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "c em", + "=> (em goal0).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [false -> ('P : prop) -> 'P]).", + "a or_e", + "=> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]] -> (not [false -> ('P : prop) -> 'P])]; [(not [[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]]) -> (not [false -> ('P : prop) -> 'P])].", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]] -> (not [false -> ('P : prop) -> 'P])]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]] -> (not [false -> ('P : prop) -> 'P])]].", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[[('P : prop) -> ['P -> false] -> (not 'P)] -> [('B : prop) -> (iff (and (or x 'B) (or x (not 'B))) x)]] -> (not [false -> ('P : prop) -> 'P])]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 990, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em and_el@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em and_i@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "intro.", + "a x0", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a x", + "=> (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x0", + "=> (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a x", + "=> (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ['P -> false] -> (not 'P)])) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "intro.", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a x0", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]).", + "a x", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]).", + "a x1", + "=> (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])) [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])))]]].", + "c x1", + "=> (x1 exfalso@type and_er@type exfalso and_er).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 312, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [(and (or x x0) (or x (not x0))) -> x]; [x -> (and (or x x0) (or x (not x0)))].", + "intro.", + "c and_er", + "=> (and_er goal0@1@1 goal0@1@2 x1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not x0)); (not x0).", + "a not_i", + "=> [(not x0) -> false].", + "c and_el", + "=> (and_el goal0@1@1 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false] -> false]].", + "c em", + "=> (em and_i@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "intro.", + "c x1", + "=> (x1 em@type not_i@type em not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> 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+ "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))) false)).", + "a x0", + "=> (and (or (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))]) (not (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))]))) (and [('P : prop) -> ['P -> false] -> (not 'P)] (and (or (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)) (not (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))) false))).", + "a x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 718, + "actions": [ + "intro.", + "c em", + "=> (em em@type).", + "intro.", + "a iff_i", + "=> [(or (and x (not x0)) (and (not x) x0)) -> (not (iff x x0))]; [(not (iff x x0)) -> (or (and x (not x0)) (and (not x) x0))].", + "intro.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a 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false) false)]; [(not [false -> ('P : prop) -> 'P]) -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)].", + "c iff_el", + "=> (iff_el p@type@1 p@type@2 p).", + "c x0", + "=> (x0 or_e@type goal1).", + "c iff_er", + "=> (iff_er p@type@1 p@type@2 p).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]]; [(not [false -> ('P : prop) -> 'P]) -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]].", + "a x", + "=> (and [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]] [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]]).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> (and [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]] [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]])]; [(not [false -> ('P : prop) -> 'P]) -> (and [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]] [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] false) false)]])].", + "intro.", + "a x", + "=> (and [(not (iff [('P : 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: prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a x5", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> 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prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "a x6" + ] + } + ], + "problem": "extrinsic_L6_7" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 2, + "evals_used": 127833, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": 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x0) (not x1))))).", + "a not_i", + "=> [(not (or (and x (and x0 x1)) (or (not x) (or (not x0) (not x1))))) -> false].", + "intro.", + "a not_e", + "=> (not (not (not (not x)))); (not (not (not x))).", + "a not_i", + "=> [(not (not (not x))) -> false].", + "intro.", + "a not_e", + "=> (not (not (not (not x)))).", + "a not_i", + "=> [(not (not (not x))) -> false].", + "intro.", + "a not_e", + "=> (not (not (not (not (not x))))); (not (not (not (not x)))).", + "a not_i", + "=> [(not (not (not (not x)))) -> false].", + "intro.", + "a not_e", + "=> (not (not (not (not (not (not x)))))); (not (not (not (not (not x))))).", + "a not_i", + "=> [(not (not (not (not (not x))))) -> false].", + "intro.", + "a not_e", + "=> (not (not (not (not (not (not (not x))))))); (not (not (not (not (not (not x)))))).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 28, + "evals_used": 127337, + "actions": [ + "intro.", + "intro.", + 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+ "c x4", + "=> (x4 or_ir@type or_ir@type or_ir).", + "c x4", + "=> (x4 iff_i@type not_i@type not_i).", + "c x4", + "=> (x4 goal4 not_i@type not_i).", + "c x4", + "=> (x4 x1 not_i@type not_i).", + "c x4", + "=> (x4 x0 not_i@type not_i).", + "c x4", + "=> (x4 goal6 not_i@type not_i).", + "c x4", + "=> (x4 x1 or_ir@type or_ir).", + "c x4", + "=> (x4 goal1 not_i@type not_i).", + "c x4", + "=> (x4 goal or_ir@type or_ir).", + "c x4", + "=> (x4 x0 or_ir@type or_ir).", + "c x4", + "=> (x4 not_i@type not_i@type not_i).", + "c x4", + "=> (x4 goal0 not_i@type not_i).", + "c x4", + "=> (x4 and_i@type not_i@type not_i).", + "c x4", + "=> (x4 goal1@2 not_i@type not_i).", + "c x4", + "=> (x4 x x0 x3).", + "c x4", + "=> (x4 iff_er@type not_i@type not_i).", + "c x4" + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..2b1ddcb1f2e8a23384b8d8121b60e34ed9e6ec2b --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,875 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 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'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=423) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L1_1 (traces=3 evals=675) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] - extrinsic_L0_9 (traces=2 evals=677) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=26) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L2_13 (traces=1 evals=128) +[OK ] g extrinsic_L3_1 (traces=1 evals=27) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L2_6 (traces=3 evals=16087) +[OK ] - extrinsic_L3_5 (traces=3 evals=1451) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L1_2 (traces=2 evals=25500) +[OK ] - extrinsic_L1_3 (traces=3 evals=25739) + +thread '' (1468396) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L3_4 (traces=8 evals=14064) + +thread '' (1468387) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L0_12 (traces=13 evals=19879) +[ ] - extrinsic_L2_2 (traces=13 evals=23084) +[ ] - extrinsic_L3_8 (traces=17 evals=30688) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] - extrinsic_L3_14 (traces=3 evals=1916) +[ ] - extrinsic_L3_7 (traces=13 evals=33076) +[ ] - extrinsic_L3_9 (traces=9 evals=17229) +[ ] - extrinsic_L3_10 (traces=17 evals=19939) +[ ] - extrinsic_L3_12 (traces=17 evals=13168) + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L3_11 (traces=16 evals=25391) +[OK ] - extrinsic_L3_18 (traces=8 evals=9327) +[ ] - extrinsic_L3_15 (traces=17 evals=21192) +[ ] - extrinsic_L3_16 (traces=11 evals=34973) +[OK ] g extrinsic_L3_23 (traces=1 evals=85) +[ ] - extrinsic_L3_17 (traces=13 evals=20902) + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=10 evals=29294) +[ ] - extrinsic_L3_20 (traces=14 evals=20905) +[ ] - extrinsic_L3_21 (traces=8 evals=31134) + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_22 (traces=15 evals=16725) + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=15 evals=22069) + +thread '' (1468399) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468396) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_27 (traces=17 evals=27093) +[ ] - extrinsic_L3_25 (traces=13 evals=21799) +[ ] - extrinsic_L3_26 (traces=14 evals=10536) + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_28 (traces=14 evals=31895) + +thread '' (1468387) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_29 (traces=13 evals=20583) +[ ] - extrinsic_L4_2 (traces=14 evals=32835) +[ ] - extrinsic_L4_1 (traces=8 evals=16499) +[ ] - extrinsic_L4_3 (traces=12 evals=18220) +[ ] - extrinsic_L4_4 (traces=7 evals=21646) +[ ] - extrinsic_L4_5 (traces=15 evals=38017) +[ ] - extrinsic_L4_6 (traces=17 evals=32257) + +thread '' (1468401) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L4_9 (traces=13 evals=35070) +[ ] - extrinsic_L4_7 (traces=13 evals=12245) +[ ] - extrinsic_L4_8 (traces=13 evals=36542) +[ ] - extrinsic_L4_10 (traces=13 evals=24226) +[ ] - extrinsic_L4_11 (traces=13 evals=50685) +[ ] - extrinsic_L4_12 (traces=13 evals=29442) +[ ] - extrinsic_L5_1 (traces=13 evals=22306) +[ ] - extrinsic_L4_13 (traces=13 evals=20342) +[ ] - extrinsic_L4_14 (traces=13 evals=42002) +[ ] - extrinsic_L5_2 (traces=13 evals=19056) + +thread '' (1468396) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468401) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_3 (traces=3 evals=27048) + +thread '' (1468401) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468401) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=16 evals=27125) +[ ] - extrinsic_L5_6 (traces=13 evals=31329) +[ ] - extrinsic_L5_5 (traces=8 evals=34695) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468394) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=11 evals=16764) +[ ] - extrinsic_L5_8 (traces=14 evals=20173) +[ ] - extrinsic_L5_9 (traces=17 evals=24900) +[ ] - extrinsic_L5_10 (traces=7 evals=19337) +[OK ] g extrinsic_L6_6 (traces=1 evals=60) + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_11 (traces=8 evals=38785) + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468398) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_3 (traces=2 evals=36670) +[ ] - extrinsic_L6_2 (traces=7 evals=39381) +[ ] - extrinsic_L6_4 (traces=16 evals=43688) +[ ] - extrinsic_L6_5 (traces=7 evals=12446) +[ ] - extrinsic_L6_7 (traces=11 evals=15856) +[ ] - extrinsic_L6_8 (traces=2 evals=127833) +[ ] - extrinsic_L6_9 (traces=1 evals=23631) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 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prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 42/94 in 5868.3s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..e5da628a28b338ed69e0ec87f61efd5f66f0a5df --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 44 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s44/train.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/train.log new file mode 100644 index 0000000000000000000000000000000000000000..6e71665440745cb2f8468d996d027c837dfc6551 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s44/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070947-7l3w9baf +[2026-06-29T07:09:43.673897] Seeded RNGs with seed=44 +[2026-06-29T07:09:43.674172] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-29T07:09:47.115462] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json + 1405 training examples loaded. + +============================================================ +[2026-06-29T07:09:47.117688] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1405 -> 1405 unique examples + Epoch 1/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 44 total steps, 1405 unique examples (batch_size=64) +[2026-06-29T07:09:56.865616] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:56.873896] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s44/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 44} diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/summary.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..15e9230aea9ff8778db1262c9e832f9e18ccb02d --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": 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-> (not (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]]) -> false].", + "intro.", + "c x4", + "=> (x4 iff_el).", + "a exfalso", + "=> false.", + "c em", + "=> (em em@type).", + "c x3", + "=> (x3 iff_i@type not_i@type iff_i not_i).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c and_el", + "=> (and_el iff_i@type not_i@type p7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 666, + "actions": [ + "intro.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> 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'P 'Q) -> ['Q -> 'P]] -> [('C : prop) -> (or x (or x0 'C)) -> (or (or x x0) 'C)]]]))).", + "c x2", + "=> (x2 iff_er).", + "c p3", + "=> (p3 x1).", + "c em", + "=> (em goal8).", + "c p3", + "=> (p3 iff_er).", + "c x2", + "=> (x2 x1).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [('C : prop) -> (or x (or x0 'C)) -> (or (or x x0) 'C)]]]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "a x1", + "=> (iff false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 331, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + 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[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)])) [x -> x0]).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))]) -> false].", + "a x5", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] -> false]).", + "a x4", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em goal20).", + "a x4", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em goal22).", + "a x5", + "=> (and (or (or x x0) x1) (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)]) (or x (or x0 x1)))] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a x5", + "=> (and [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (and (or 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x0)].", + "c em", + "=> (em x0).", + "intro.", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5157, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_e", + "=> [x -> (or (or x x0) x1)]; [(or x0 x1) -> (or (or x x0) x1)].", + "intro.", + "a or_ir", + "=> x1.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x5", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [x -> (or (or x x0) x1)]); [[[('P : 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "c x1", + "=> (x1 p0@type).", + "a not_e", + "=> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])))); (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (not (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))))].", + "c x1", + "=> (x1 x0@type).", + "c x2", + "=> (x2 goal not_i@type not_i).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [(not [('P : prop) -> (or 'P (not 'P))]) -> false].", + "a or_e", + "=> [(iff x (not x)) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]]; [(not (iff x (not x))) -> [(not [('P : prop) -> (or 'P (not 'P))]) -> false]].", + "c em", + "=> (em goal4).", + "c x2", + "=> (x2 or_e@type not_e@type not_e).", + "intro.", + "intro.", + "a or_e", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[[('P : prop) -> (or 'P (not 'P))] -> false] -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]]; [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]].", + "intro.", + "a exfalso", + "=> false.", + "c not_e", + "=> (not_e em@type x4 em).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(not [[('P : prop) -> (or 'P (not 'P))] -> false]) -> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false]]].", + "c x2", + "=> (x2 x0@type goal1 x4).", + "a exfalso", + "=> false.", + "c iff_er", + "=> (iff_er x x0@type@2 x3).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 300, + "actions": [ + "intro.", + "intro.", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "intro.", + "c em", + "=> (em not_i@type).", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em p0@type).", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a x1", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3213, + "actions": [ + "intro.", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(iff x (not x)) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(iff x (not x)) -> false]].", + "intro.", + "intro.", + "c iff_el", + "=> (iff_el x x1@type@2 x1).", + "c em", + "=> (em or_il@type).", + "a x0", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c iff_er", + "=> (iff_er x x1@type@2 x1).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a x0", + "=> false.", + "a x0", + "=> false.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 not_i@type p1@type not_i).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x2", + "=> (x2 p0@type or_e@type p0).", + "c x3", + "=> (x3 exfalso@type or_ir@type exfalso).", + "intro.", + "a not_e", + "=> (not [x -> (not x)]).", + "c x3", + "=> (x3 iff_er@type and_el@type iff_er).", + "a not_i", + "=> [[x -> (not x)] -> false].", + "c em", + "=> (em goal20).", + "c em", + "=> (em p4@type).", + "intro.", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 364, + "actions": [ + "intro.", + "intro.", + "a not_e", + "=> (not [('A : prop) -> (iff 'A (not 'A)) -> false]); [('A : prop) -> (iff 'A (not 'A)) -> false].", + "a not_i", + "=> [[('A : prop) -> (iff 'A (not 'A)) -> false] -> false].", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "intro.", + "c x1", + "=> (x1 x x0).", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "c iff_el", + "=> (iff_el x x0@type@2 x0).", + "intro.", + "intro.", + "a not_e", + "=> (not (iff x (not x))).", + "a not_i", + "=> [(iff x (not x)) -> false].", + "intro.", + "c iff_er", + "=> (iff_er x1 x2@type@2 x2).", + "a not_e", + "=> (not (iff x (not x))).", + "a not_i", + "=> [(iff x (not x)) -> false].", + "intro.", + "c iff_er", + "=> (iff_er x x0@type@2 x4).", + "c em", + "=> (em iff_el@type).", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (not x1)); (not x1).", + "a not_i", + "=> [(not x1) -> false].", + "c iff_el", + "=> (iff_el x x0@type@2 x3).", + "intro.", + "c p1", + "=> (p1 x5).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]].", + "c iff_er", + "=> (iff_er x x0@type@2 x3).", + "c iff_el", + "=> (iff_el x x0@type@2 x4).", + "c iff_el", + "=> (iff_el x1 x2@type@2 x2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false]]].", + "c p9", + "=> (p9 p6).", + "intro.", + "c x6" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 698, + "actions": [ + "a exfalso", + "=> false.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]].", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]]]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p@type and_i@type p and_i).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]].", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p@type and_i@type p2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) -> false].", + "c 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(not 'P)]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 and_i@type and_er@type and_i and_er).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c and_el", + "=> (and_el and_i@type and_er@type p0).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em p@type@2).", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em goal9).", + "c x3", + "=> (x3 iff_i@type not_e@type iff_i not_e).", + "intro.", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]].", + "a or_e", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]; [(not (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]].", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]]; [(not (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]]]].", + "c and_er", + "=> (and_er iff_i@type not_e@type p5).", + "c and_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 643, + "actions": [ + "intro.", + "intro.", + "a or_ir", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]].", + "intro.", + "c em", + "=> (em x0).", + "a or_e", + "=> [x0 -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]]; [(not x0) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]]].", + "c em", + "=> (em goal4).", + "intro.", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]).", + "a x3", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))].", + "intro.", + "a or_e", + "=> [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not x0) -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))].", + "a x3", + "=> (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))).", + "c em", + "=> (em not_i@type).", + "a x3", + "=> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))].", + "c em", + "=> (em goal17).", + "a x2", + "=> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or x0 (not x0))).", + "a or_e", + "=> [x0 -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or x0 (not x0)))]; [(not x0) -> (and [[('P : prop) -> ['P -> false] -> (not 'P)] -> (and (and [x0 -> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]] [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))) (not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]))] (or x0 (not x0)))].", + "a exfalso", + "=> false.", + "c em", + "=> (em p2@type).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a x5", + "=> (and (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]).", + "a and_i", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3737, + "actions": [ + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a or_il", + "=> x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [x -> x0]); [x -> x0].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not [x -> x0])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (not [x -> x0])].", + "intro.", + "c x1", + "=> (x1 and_el@type and_el@type and_el and_el).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em em@type).", + "intro.", + "c and_el", + "=> (and_el and_el@type and_el@type p0).", + "a p2", + "=> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))).", + "c x1", + "=> (x1 and_i@type iff_i@type x1 iff_i).", + "a or_e", + "=> [[('P : prop) -> (or 'P (not 'P))] -> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))]; [(not [('P : prop) -> (or 'P (not 'P))]) -> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))].", + "a p2", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))] (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (and [[('P : prop) -> (or 'P (not 'P))] -> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))] (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> (and [[('P : prop) -> (or 'P (not 'P))] -> (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])))] (and false (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el and_i@type iff_i@type p3).", + "c em", + "=> (em x0).", + "a not_e", + "=> (not (or x [x -> x0])); (or x [x -> x0]).", + "a not_i", + "=> [(or x [x -> x0]) -> false].", + "c x2", + "=> (x2 p0@type and_el@type p0 and_el).", + "c em", + "=> (em goal13).", + "c x1", + "=> (x1 p6@type p0@type p6 p0).", + "c x3", + "=> (x3 p6@type or_e@type p6 or_e).", + "c p4", + "=> (p4 p3@type and_i@type p3 and_i).", + "c and_el" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 453, + "actions": [ + "intro.", + "intro.", + "a or_il", + "=> x.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "c em", + "=> (em p@type).", + "intro.", + "a x2", + "=> false.", + "a not_e", + "=> (not (or x [x -> x0])); (or x [x -> x0]).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (or x [x -> x0]))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (not (or x [x -> x0]))].", + "a exfalso", + "=> false.", + "a x1", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x2", + "=> false.", + "a not_e", + "=> (not (not false)); (not false).", + "a or_e", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not false))]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> (not (not false))].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not false))]]; [(not (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false]))) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not false))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not false))]]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) -> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> (not (not false))]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "a or_e", + "=> [false -> false]; [(not false) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2898, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "a or_ir", + "=> [x -> x0].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "c em", + "=> (em not_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not [('P : prop) -> (or 'P (not 'P))])].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not [('P : prop) -> (or 'P (not 'P))])]].", + "intro.", + "intro.", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "c x2", + "=> (x2 not_e@type goal4 not_e).", + "intro.", + "a x1", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]))).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not (or [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])))]].", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c x3", + "=> (x3 x).", + "c x3", + "=> (x3 goal3).", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 iff_el@type p0@type iff_el).", + "a not_e", + "=> (not x0); x0.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not x0)]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not x0)].", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 exfalso@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "c x2", + "=> (x2 and_i@type iff_er@type and_i).", + "c em", + "=> (em iff_i@type).", + "c x2" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 325, + "actions": [ + "intro.", + "intro.", + "a or_il", + "=> x.", + "a exfalso", + "=> false.", + "c em", + "=> (em goal).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])]) -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> 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false) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]; [(not (not false)) -> [(not false) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]].", + "c em", + "=> (em p0@type).", + "intro.", + "intro.", + "a exfalso", + "=> .", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[false -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]] -> [(not (not false)) -> [(not false) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]; [(not [false -> [false -> [[('A : prop) -> ('B 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[[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]; [(not (not false)) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]].", + "a or_e", + "=> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]; [(not (not false)) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]].", + "a or_e", + "=> [false -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]]; [(not false) -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]].", + "a or_e", + "=> [false -> [false -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]]]; [(not false) -> [false -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]]].", + "a or_e", + "=> [(not false) -> [false -> [false -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]]]]; [(not (not false)) -> [false -> [false -> [(not false) -> [(not false) -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [(not (not false)) -> [false -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> [[('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] -> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]]]]]]]]]].", + "intro.", + "c not_e", + "=> (not_e false x3 x2).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2383, + "actions": [ + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em iff_er@type).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x", + "=> false.", + "a x", + "=> false.", + "c em", + "=> (em goal2).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] 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not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "intro.", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a iff_i", + "=> [false -> [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "a x0", + "=> (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal5).", + "c em", + "=> (em and_er@type).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c x1", + "=> (x1 and_el@type iff_el@type and_el iff_el).", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))).", + "c and_er", + "=> (and_er and_el@type iff_el@type p2).", + "c em", + "=> (em p1@type).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5604, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em and_el@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "intro.", + "a not_e", + "=> (not (not [x -> (not x)])).", + "a not_i", + "=> [(not [x -> (not x)]) -> false].", + "intro.", + "a x3", + "=> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [(not x) -> false]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])].", + "a x2", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a x3", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])].", + "c em", + "=> (em goal14).", + "a x2", + "=> (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) x).", + "a x2", + "=> (and (and (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]) x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])); (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]]; [(not [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])]) -> [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]]].", + "intro.", + "a x2", + "=> (and [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or (not x) [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))]] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a x3", + "=> (or (or [('P : prop) -> 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['Q -> 'P] -> (iff 'P 'Q)] -> x]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x]]]]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x]]].", + "c em", + "=> (em goal9).", + "c em", + "=> (em goal0@2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> x]]]]] -> [[[('P : 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-> x].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a x3", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 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: prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [(not [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]) -> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]] false) (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]] false)))]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]] false) (and [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))]] false)))].", + "c x4", + "=> (x4 and_el@type iff_i@type and_el iff_i).", + "a x2" + ] + } + ], + "problem": "extrinsic_L5_2" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 17, + "evals_used": 28684, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 287, + "actions": [ + "intro.", + "intro.", + "a iff_i", + "=> [(or (and x x0) (and x (not x0))) -> x]; [x -> (or (and x x0) (and x (not x0)))].", + "intro.", + "a or_e", + "=> [(and x x0) -> x]; [(and x (not x0)) -> x].", + "intro.", + "c and_er", + "=> (and_er x x0 x2).", + "c and_el", + "=> (and_el x x0 x2).", + "intro.", + "c and_er", + "=> (and_er x goal0@1@2@2 x2).", + "c and_el", + "=> (and_el x goal0@1@2@2 x2).", + "intro.", + "a or_ir", + "=> (and x (not x0)).", + "a and_i", + "=> (not x0).", + 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'Q)] -> false]].", + "c em", + "=> (em goal).", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em false).", + "c em", + "=> (em p6@type).", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em p6@type@2).", + "c em", + "=> (em goal2).", + "a or_e", + "=> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]; [(not (or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))]))) -> false].", + "c em", + "=> (em x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [(or [('P : prop) -> (or 'P (not 'P))] (not [('P : prop) -> (or 'P (not 'P))])) -> false]].", + "c em", + "=> (em and_el@type).", + "a exfalso", + "=> 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[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]]]].", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 p@type and_i@type p and_i).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el p@type and_i@type p2).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]]) -> false].", + "c em", + "=> (em or_e@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]] -> false]]; [(not [('P : prop) -> ('Q : prop) 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: prop) -> (and 'P 'Q) -> 'Q] -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))]))))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (and (not [('P : prop) -> ('Q : prop) -> 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prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))])))).", + "a x3", + "=> (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(and x (not x0)) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0))))] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))]) (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))]))))).", + "c x3", + "=> (x3 x goal0@1@1@2 x4).", + "c em", + "=> (em goal21).", + "a x5", + "=> (and (or [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))] (not [(and x (not x0)) -> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0)))))])) (and [('P : prop) -> (not 'P) -> 'P -> false] (and [(and x (not x0)) -> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (or (and x (not x0)) (and (not x) x0)) (not (iff x x0))))] (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (and (and [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] 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(not (or [x -> x0] [x0 -> x1]))]]; [[x0 -> x1] -> [x -> (not (or [x -> x0] [x0 -> x1]))]].", + "c x4", + "=> (x4 x7).", + "a or_e", + "=> [x -> [[x -> x0] -> [x -> (not (or [x -> x0] [x0 -> x1]))]]]; [(not x) -> [[x -> x0] -> [x -> (not (or [x -> x0] [x0 -> x1]))]]].", + "intro.", + "intro.", + "c x4", + "=> (x4 x8).", + "c x9", + "=> (x9 x8).", + "intro.", + "c x4", + "=> (x4 x10).", + "a or_e", + "=> [[x -> x0] -> (not (or [x -> x0] [x0 -> x1]))]; [[x0 -> x1] -> (not (or [x -> x0] [x0 -> x1]))].", + "c x5", + "=> (x5 x10).", + "a or_e", + "=> [[x -> x0] -> [[x -> x0] -> (not (or [x -> x0] [x0 -> x1]))]]; [[x0 -> x1] -> [[x -> x0] -> (not (or [x -> x0] [x0 -> x1]))]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 788, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_il", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em and_er@type).", + "c em", + "=> (em and_el@type).", + "a or_e", + 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[[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]].", + "intro.", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]).", + "a x4", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)])).", + "a exfalso", + "=> false.", + "a x3", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false).", + "a x4", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false))).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false)))).", + "a x3", + "=> (and (or [x -> x0] [x0 -> x1]) (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)] (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]) (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) false))))).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]].", + "intro.", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]).", + "a x4", + "=> (and [false -> ('P : prop) -> 'P] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]])).", + "a x3", + "=> (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)])) (and [false -> ('P : prop) -> 'P] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]))).", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> x0] (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)])) (and [false -> ('P : prop) -> 'P] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]])))).", + "a x5", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> x0] (and (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)]] [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) x0)])) (and [false -> ('P : prop) -> 'P] (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]]] [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [('P : prop) -> ['P -> false] -> (not 'P)])]])))) [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5335, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_il", + "=> [x -> x0].", + "intro.", + "c em", + "=> (em x).", + "a 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('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))) -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "dead", + "depth_used": 46, + "evals_used": 241, + "actions": [ + "intro.", + "intro.", + "intro.", + "a iff_i", + "=> [(iff x (iff x0 x1)) -> (iff (iff x x0) x1)]; [(iff (iff x x0) x1) -> (iff x (iff x0 x1))].", + "intro.", + "a iff_i", + "=> [(iff x x0) -> x1]; [x1 -> (iff x x0)].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [(iff x x0) -> x1]); [(iff x x0) -> x1].", + "c iff_er", + "=> (iff_er x goal0@1@2 x2).", + "a not_i", + "=> [[(iff x x0) -> x1] -> false].", + "intro.", + "c iff_el", + "=> (iff_el x goal0@1@2 x2).", + "a not_e", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (iff x0 x1)); (iff x0 x1).", + "a not_i", + "=> [(iff x0 x1) -> false].", 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-> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "a or_e", + "=> [false -> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]]; [(not false) -> [false -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]].", + "intro.", + "intro.", + "c em", + "=> (em p4@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]].", + "c em", + "=> (em p8@type@2).", + "intro.", + "c x4" + ] + }, + { + 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[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (or (not x0) (not x1)))].", + "c x2", + "=> (x2 not_e@type goal4 goal0@1@2).", + "intro.", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 p0@type@2@2@1 false goal)." + ] + } + ], + "problem": "extrinsic_L6_8" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 1, + "evals_used": 126302, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 27, + "evals_used": 126302, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "c em", + "=> (em goal).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> x1]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> x1].", + "intro.", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> x1]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> x1].", + "intro.", + "c x4", + "=> (x4 or_ir@type or_ir@type or_ir@type).", + "c x4", + "=> (x4 goal or_ir@type goal4).", + "c x4", + "=> (x4 x x x).", + "c x4", + "=> (x4 x x goal).", + "c x4", + "=> (x4 goal x goal4).", + "c x4", + "=> (x4 x or_ir@type x)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..639bc6bde05d4a1a5703465d11776f846b1c977f --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,884 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=408) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L0_9 (traces=2 evals=531) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=47) +[OK ] - extrinsic_L1_1 (traces=3 evals=788) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] - extrinsic_L2_9 (traces=2 evals=548) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L2_13 (traces=1 evals=121) +[OK ] g extrinsic_L3_1 (traces=1 evals=27) +[OK ] - extrinsic_L2_6 (traces=3 evals=700) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] - extrinsic_L3_5 (traces=2 evals=459) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L3_4 (traces=2 evals=677) +[OK ] - extrinsic_L1_2 (traces=2 evals=25092) +[OK ] - extrinsic_L1_3 (traces=3 evals=25705) +[OK ] - extrinsic_L3_10 (traces=5 evals=8827) +[OK ] - extrinsic_L0_12 (traces=6 evals=10325) +[OK ] - extrinsic_L3_12 (traces=3 evals=822) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[OK ] - extrinsic_L3_11 (traces=4 evals=1398) +[OK ] - extrinsic_L3_14 (traces=3 evals=2814) + +thread '' (1468393) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L2_2 (traces=17 evals=27411) +[OK ] g extrinsic_L3_17 (traces=1 evals=67) +[OK ] - extrinsic_L3_18 (traces=3 evals=2938) + +thread '' (1468402) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468402) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468393) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_7 (traces=13 evals=15322) +[ ] - extrinsic_L3_8 (traces=13 evals=16810) +[OK ] - extrinsic_L3_9 (traces=8 evals=20921) +[ ] - extrinsic_L3_15 (traces=7 evals=11007) +[OK ] g extrinsic_L3_23 (traces=1 evals=33) +[ ] - extrinsic_L3_16 (traces=17 evals=25090) + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_19 (traces=13 evals=16750) +[ ] - extrinsic_L3_21 (traces=17 evals=24973) + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=17 evals=19908) +[ ] - extrinsic_L3_20 (traces=17 evals=21542) +[ ] - extrinsic_L3_22 (traces=15 evals=15020) + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_25 (traces=17 evals=14175) + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_1 (traces=17 evals=17753) +[ ] - extrinsic_L3_26 (traces=11 evals=9983) + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_27 (traces=17 evals=24489) + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_29 (traces=12 evals=20166) +[ ] - extrinsic_L3_28 (traces=11 evals=18261) +[ ] - extrinsic_L4_2 (traces=6 evals=11369) +[ ] - extrinsic_L4_4 (traces=17 evals=26962) + +thread '' (1468393) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=13 evals=35495) +[ ] - extrinsic_L4_5 (traces=15 evals=27480) +[ ] - extrinsic_L4_8 (traces=17 evals=35887) +[ ] - extrinsic_L4_6 (traces=15 evals=24058) + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_7 (traces=12 evals=17913) +[ ] - extrinsic_L4_9 (traces=13 evals=23990) +[ ] - extrinsic_L4_10 (traces=17 evals=37617) +[ ] - extrinsic_L4_11 (traces=10 evals=28885) +[ ] - extrinsic_L4_12 (traces=14 evals=37990) +[ ] - extrinsic_L4_14 (traces=13 evals=61415) +[ ] - extrinsic_L4_13 (traces=11 evals=20464) + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_1 (traces=8 evals=20377) +[ ] - extrinsic_L5_6 (traces=17 evals=13917) +[ ] - extrinsic_L5_2 (traces=13 evals=17615) +[ ] - extrinsic_L5_3 (traces=17 evals=28684) + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=13 evals=22913) +[ ] - extrinsic_L5_5 (traces=13 evals=44714) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_7 (traces=17 evals=14874) + +thread '' (1468397) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468402) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=8 evals=29240) + +thread '' (1468393) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=14 evals=20326) + +thread '' (1468393) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=14 evals=22801) +[OK ] g extrinsic_L6_6 (traces=1 evals=61) + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468395) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_11 (traces=17 evals=38786) + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1468388) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_2 (traces=17 evals=23201) + +thread '' (1468400) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L6_3 (traces=16 evals=18198) +[ ] - extrinsic_L6_5 (traces=12 evals=15915) +[ ] - extrinsic_L6_7 (traces=4 evals=7122) +[ ] - extrinsic_L6_4 (traces=15 evals=102557) +[ ] - extrinsic_L6_9 (traces=1 evals=126302) +[ ] - extrinsic_L6_8 (traces=10 evals=102173) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 47/94 in 5143.7s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..e5da628a28b338ed69e0ec87f61efd5f66f0a5df --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 44 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s45/train.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/train.log new file mode 100644 index 0000000000000000000000000000000000000000..504c12cdfef4ea1d62a14064ee3d9c189a91f3ac --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s45/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_070948-0vpu5z3b +[2026-06-29T07:09:43.597491] Seeded RNGs with seed=45 +[2026-06-29T07:09:43.597771] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-29T07:09:47.529829] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json + 1405 training examples loaded. + +============================================================ +[2026-06-29T07:09:47.532039] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1405 -> 1405 unique examples + Epoch 1/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 44 total steps, 1405 unique examples (batch_size=64) +[2026-06-29T07:09:57.267206] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:09:57.279610] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s45/2026-06-29_07-09-43/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 44} diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/summary.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/summary.json new file mode 100644 index 0000000000000000000000000000000000000000..c783ee86263a3973fd6358d580c54167ec39e4a8 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/summary.json @@ -0,0 +1,18 @@ +{ + "checkpoint": "/datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt", + "examples": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json", + "configs": [ + { + "mode": "epoch", + "batch_size": 64, + "n_epochs": 2, + "save_every": 1 + } + ], + "results": { + "updates_1_epoch_2ep_bs64": { + "path": "/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt", + "total_gradient_steps": 44 + } + } +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt new file mode 100644 index 0000000000000000000000000000000000000000..826e051f9e40597d941573c3b140f30bd9f14a0f --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt @@ -0,0 +1,3 @@ +version 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> (or 'A (not 'A))]); [('A : prop) -> (or 'A (not 'A))].", + "a not_i", + "=> [[('A : prop) -> (or 'A (not 'A))] -> false].", + "intro.", + "c x0", + "=> (x0 iff_er@type).", + "c x0", + "=> (x0 exfalso@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "c x0", + "=> (x0 or_ir@type).", + "c em", + "=> (em goal1).", + "c em", + "=> (em p1@type@2).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "intro.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]; [(not [false -> ('P : prop) -> 'P]) -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]].", + "a x3", + "=> (iff [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a iff_i", + "=> [[[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]] -> [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]).", + "a or_e", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]])]; [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])) -> (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]])].", + "a x1", + "=> (iff (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])).", + "c em", + "=> (em or_ir@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff (iff [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [[false -> ('P : prop) -> 'P] -> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false]]) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x3" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3551, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "intro.", + "intro.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ['P -> false] -> (not 'P)])); (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c x0", + "=> (x0 exfalso@type p@type@2 exfalso).", + "a exfalso", + "=> false.", + "c x0", + "=> (x0 iff_el@type p@type iff_el).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c x0", + "=> (x0 or_il@type goal7 x0).", + "c x1", + "=> (x1 and_i@type goal and_i).", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> false]].", + "c em", + "=> (em x).", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "intro.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]].", + "c em", + "=> (em goal16).", + "c x0", + "=> (x0 p@type and_er@type p).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> [[false -> ('P : prop) -> 'P] -> false]]]].", + "c em", + "=> (em p@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4044, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "intro.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a not_i", + "=> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false].", + "a x1", + "=> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); [[false -> ('P : prop) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]); [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [[[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]] -> (or [false -> ('P : prop) -> 'P] (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "a or_il", + "=> .", + "c x0", + "=> (x0 and_er@type not_e@type and_er not_e).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c em", + "=> (em goal).", + "intro.", + "c and_el", + "=> (and_el and_er@type not_e@type p0).", + "a p2", + "=> (and (not [('A : prop) -> (or 'A (not 'A))]) false).", + "c x0", + "=> (x0 and_i@type p0@type x0 p0).", + "c and_er", + "=> (and_er and_er@type not_e@type p0).", + "a p2", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('A : prop) -> (or 'A (not 'A))]) false)).", + "a or_e", + "=> [[('A : prop) -> (or 'A (not 'A))] -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('A : prop) -> (or 'A (not 'A))]) false))]; [(not [('A : prop) -> (or 'A (not 'A))]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and (not [('A : prop) -> (or 'A (not 'A))]) false))].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el and_i@type p0@type p3).", + "c em", + "=> (em goal0).", + "a not_e", + "=> (not (not (or x (not x)))); (not (or x (not x))).", + "a not_i", + "=> [(not (or x (not x))) -> false].", + "a x1", + "=> (or [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(not (or x (not x))) -> false]]; [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [(not (or x (not x))) -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 462, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not x)]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not x)].", + "intro.", + "a not_i", + "=> [x -> false].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c em", + "=> (em iff_i@type).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x2", + "=> (iff false [('P : prop) -> (not 'P) -> 'P -> false]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff false [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (iff false [('P : prop) -> (not 'P) -> 'P -> false])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (iff false [('P : prop) -> (not 'P) -> 'P -> false])]]; [(not 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false)).", + "c x3", + "=> (x3 iff_er@type p2@type p2).", + "a not_i" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 712, + "actions": [ + "intro.", + "intro.", + "intro.", + "a and_i", + "=> (not x); (not x0).", + "a not_i", + "=> [x -> false].", + "intro.", + "c em", + "=> (em and_el@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false).", + "a x3", + "=> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)).", + "c not_e", + "=> (not_e x x4 x2).", + "a x3", + "=> (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))).", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false)))).", + "c em", + "=> (em goal11).", + "a x3", + "=> (and (not x) (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false] (and (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])) (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (and [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] false))))).", + "c em", + "=> (em or_il@type).", + "a exfalso", + "=> .", + "a not_i", + "=> 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false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "a x2", + "=> false.", + "a not_e", + "=> (not (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))).", + "c x1", + "=> (x1 goal5).", + "a not_i", + "=> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) -> false].", + "c em", + "=> (em p4@type@2).", + "intro.", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> false]; [(not (not (not [('P : prop) -> (or 'P (not 'P))]))) -> false].", + "intro.", + "a or_e", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> false]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> false].", + "c x1", + "=> (x1 x0).", + "a or_e", + "=> [(not (not [('P : prop) -> (or 'P (not 'P))])) -> [(or [('P : prop) -> ['P -> false] -> (not 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-> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))] -> (and (not [('P : prop) -> (not 'P) -> 'P -> false]) [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(and (not [('P : prop) -> (not 'P) -> 'P -> false]) [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(and (not [('P : prop) -> (not 'P) -> 'P -> false]) [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]]].", + "a x4", + "=> (iff [(and (not [('P : prop) -> (not 'P) -> 'P -> false]) [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c em", + "=> (em goal21).", + "a x3", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (iff [(and (not [('P : prop) -> (not 'P) -> 'P -> false]) [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]) -> [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (and [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) (and (or [('P : prop) -> (not 'P) -> 'P -> false] (not [('P : prop) -> (not 'P) -> 'P -> false])) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])))]] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 376, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] false).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a x", + "=> (and [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] false).", + "a and_i", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a x", + "=> (and false (not [false -> ('P : prop) -> 'P])).", + "a and_i", + "=> false; (not [false -> ('P : prop) -> 'P]).", + "a not_e", + "=> (not (not [false -> ('P : prop) -> 'P])); (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> false].", + "a exfalso", + 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[x -> false]]]]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not x) -> [x -> [(not x) -> [x -> false]]]]]]].", + "c em", + "=> (em goal0@1).", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[[(not x) -> [x -> [(not x) -> [x -> false]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not x) -> [x -> [(not x) -> [x -> false]]]]]]] -> [[(not x) -> [x -> [(not x) -> [x -> false]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not x) -> [x -> [(not x) -> [x -> false]]]]]]]]; [(not [[(not x) -> [x -> [(not x) -> [x -> false]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not x) -> [x -> [(not x) -> [x -> false]]]]]]]) -> [[(not x) -> [x -> [(not x) -> [x -> false]]]] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [x -> [(not x) -> [x -> [(not x) -> [x -> false]]]]]]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal2).", + "a or_e", + "=> [[[(not x) -> [x -> 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(and 'P 'Q) -> 'P]))).", + "c em", + "=> (em goal12).", + "a x", + "=> (and (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])).", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x0", + "=> (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> 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false) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false])).", + "a x0", + "=> (and (not (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (and [false -> ('P : prop) -> 'P] (and (and (and (and (and false [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) false) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]))).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3280, + "actions": [ + "intro.", + "a iff_i", + "=> [(not x) -> [x -> false]]; [[x -> false] -> (not x)].", + "intro.", + "intro.", + "c not_e", + "=> (not_e x x0 x1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 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-> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em and_el@type).", + "c em", + "=> (em p5@type).", + "intro.", + "c em", + "=> (em and_i@type).", + "c em", + "=> (em p4@type).", + "a x2", + "=> (or (not false) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])); [(not false) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "a x2", + "=> (or (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (not false) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (not false) (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]))]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 456, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em iff_i@type).", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c and_el", + "=> (and_el x x2@type@2 x2).", + "a not_e", + "=> (not (and x x0)); (and x x0).", + "a not_i", + "=> [(and x x0) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c and_er", + "=> (and_er x x0 x3).", + "intro.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])); (not [('P : prop) -> ('Q : 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-> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))]); [(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))].", + "a x1", + "=> [[(not (not [('P : prop) -> (not 'P) -> 'P -> false])) -> (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))] -> false]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5762, + "actions": [ + "intro.", + "c em", + "=> (em iff_er@type).", + "intro.", + "c iff_er", + "=> (iff_er x x0@type@2 x0).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c x1", + "=> (x1 or_il@type 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'P -> (or 'P 'Q)] -> (not (iff x (not x)))]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> (not (iff x (not x)))].", + "c x1", + "=> (x1 or_e@type and_er@type or_e).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff x (not x)))]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff x (not x)))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff x (not x)))]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (iff x (not x)))]]].", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "c em", + "=> (em iff_el@type).", 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['P -> false] -> (not 'P)] -> false]].", + "a x1", + "=> [[(not [x -> (not x)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false].", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> [[(not [x -> (not x)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> [[(not [x -> (not x)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> false]].", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em exfalso@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "intro.", + "a x8", + "=> false.", + "a not_e", + "=> (not (not [x -> (not x)])); (not [x -> (not x)]).", + "a exfalso" + ] + }, + { + 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[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em", + "=> (em goal4).", + "c em", + "=> (em p0@type).", + "intro.", + "c x1", + "=> (x1 false or_ir@type x1).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]]; [[('P : prop) -> (or 'P (not 'P))] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]]].", + "intro.", + "intro.", + "a x4", + "=> (iff [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "c em", + "=> (em or_il@type).", + "a x3", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[('P : prop) -> ('Q : prop) -> 'Q 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"intro.", + "a or_e", + "=> [(iff x (not (not x))) -> [(iff x (not (not x))) -> false]]; [(not (iff x (not (not x)))) -> [(iff x (not (not x))) -> false]].", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 56, + "evals_used": 2143, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em and_el@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false]].", + "intro.", + "intro.", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false].", + "a x1", + "=> (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "c em", + "=> (em iff_el@type).", + "a x1", + "=> (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a x1", + "=> (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]).", + "a x0", + "=> (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])).", + "a x1", + "=> (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x0", + "=> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])).", + "c em", + "=> (em em@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))].", + "intro.", + "a and_i", + "=> (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]); (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] -> (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "a x1", + "=> (and (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]))] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a x", + "=> (and (and (or [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (and (and (and (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))]) (and (and (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> (or 'P (not 'P))])) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 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prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3697, + "actions": [ + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a not_e", + "=> (not [(not (not x)) -> x]); [(not (not x)) -> x].", + "a x0", + "=> (or [('A : prop) -> [(not (not 'A)) -> 'A]] [('P : 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-> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])]; [(not (iff [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false] [[('P : prop) -> (not 'P) -> 'P -> false] -> [('A : prop) -> [(not (not 'A)) -> 'A]]])) -> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])].", + "c em" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 9766, + "actions": [ + "c em", + "=> (em and_i@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> [('A : prop) -> [(not (not 'A)) -> 'A]]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [('A : prop) -> [(not (not 'A)) -> 'A]]].", + "intro.", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x0]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x0].", + "intro.", + "c x2", + "=> (x2 or_ir@type x1@type or_ir x1).", + "c x2", + "=> (x2 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-> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> false].", + "c x1", + "=> (x1 not_i@type and_er@type and_er).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) -> false].", + "c x1", + "=> (x1 p@type@2 x0@type x0).", + "intro.", + "c x2", + "=> (x2 or_ir).", + "intro.", + "c x1", + "=> (x1 goal6 or_e@type or_e).", + "c x1", + "=> (x1 and_er@type p@type p).", + "c em", + "=> (em em@type).", + "a not_e", + "=> (not x).", + "c x1", + "=> (x1 iff_i@type and_el@type and_el).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not x)].", + "c x1", + "=> (x1 exfalso@type p1@type p1).", + "c x1", + "=> (x1 and_er@type and_er@type and_er).", + "c x1", + "=> (x1 goal11 exfalso@type exfalso).", + "intro.", + "a not_i", + "=> [x -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [x -> false]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [x -> false]].", + "c em", + "=> (em not_i@type).", + "c em", + "=> (em false).", + "intro.", + "intro." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5657, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> x].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x); x.", + "c em", + "=> (em not_i@type).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> (not x)].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not x)]].", + "c x1", + "=> (x1 x0@type iff_er@type x0).", + "c em", + "=> (em or_ir@type).", + "c em", + "=> (em p0@type@2).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em p@type).", + "a not_e", + "=> (not (not (not [('P : prop) -> ['P -> false] -> (not 'P)]))); (not (not [('P : prop) -> ['P -> false] -> (not 'P)])).", + "c x2", + "=> (x2 and_i@type exfalso@type and_i).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "a not_e", + "=> 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+ "=> (em iff_i@type).", + "c x1" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 483, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x).", + "c em", + "=> (em iff_er@type).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not [(not (not x)) -> x]); [(not (not x)) -> x].", + "a not_i", + "=> [[(not (not x)) -> x] -> false].", + "intro.", + "c em", + "=> (em or_e@type).", + "c em", + "=> (em or_ir@type).", + "a not_e", + "=> (not [('A : prop) -> [(not (not 'A)) -> 'A]]); [('A : prop) -> [(not (not 'A)) -> 'A]].", + "a exfalso", + "=> false.", + "c x2", + "=> (x2 x0).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em goal7).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em goal9).", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]).", + "c em", + "=> (em p0@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]; [(not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]].", + "a or_e", + "=> [(not [('A : prop) -> [(not (not 'A)) -> 'A]]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]; [(not (not [('A : prop) -> [(not (not 'A)) -> 'A]])) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]].", + "a or_e", + "=> [[[(not (not x)) -> x] -> false] -> [(not [('A : prop) -> [(not (not 'A)) -> 'A]]) -> [(or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]]]]; [(not [[(not (not x)) -> 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not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[x -> x0] -> [(not x) -> x0] -> x0]]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[x -> x0] -> [(not x) -> x0] -> x0]].", + "a or_e", + "=> [[[x -> x0] -> [(not x) -> x0] -> x0] -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[x -> x0] -> [(not x) -> x0] -> x0]])]; [(not [[x -> x0] -> [(not x) -> x0] -> x0]) -> (not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[x -> x0] -> [(not x) -> x0] -> x0]])].", + "c em", + "=> (em p7@type@2)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 4313, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false].", + "intro.", + "a x", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a x", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> (not [('P : prop) -> (not 'P) -> 'P -> false])]; [(not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]) -> (not [('P : prop) -> (not 'P) -> 'P -> false])].", + "a exfalso", + "=> false.", + "a x", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> false].", + "intro.", + "a x1", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "c x2", + "=> (x2 or_ir@type or_il@type x0).", + "c x0", + "=> (x0 and_i@type iff_i@type and_i).", + "a not_e", + "=> (not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]); [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "c x0", + "=> (x0 not_e@type goal11 x1).", + "a not_i", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> false].", + "intro.", + "c x2", + "=> (x2 goal11 or_il@type x0).", + "a x1", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]; [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))].", + "a x", + "=> [[[('P : prop) -> (not 'P) -> 'P -> false] -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]]; [(not [[('P : prop) -> (not 'P) -> 'P -> false] -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]))]].", + "c x3", + "=> (x3 x1).", + "intro.", + "c x0", + "=> (x0 goal and_er@type x).", + "intro.", + "c em", + "=> (em p0@type).", + "c x5", + "=> (x5 or_e@type false or_e p4).", + "a or_e" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 5287, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "c em", + "=> (em and_el@type).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false].", + "intro.", + "a x3", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c em", + "=> (em and_i@type).", + "a or_ir", + "=> .", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]].", + "intro.", + "a x4", + "=> (and [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a x4", + "=> (and (and [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (and [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", + "a exfalso", + "=> false.", + "a x4", + "=> (and false [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a x4", + "=> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]]).", + "a x3", + "=> (or [(not x) -> x0] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])); [[(not x) -> x0] -> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false] -> false]])].", + "a x3", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [(not x) -> x0] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))]; [[false -> ('P : prop) -> 'P] -> (or [(not x) -> x0] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))].", + "a x3", + "=> (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P])]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [x -> x0]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [x -> x0])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "a x4", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]).", + "a x4", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]).", + "a x4", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]) (not [x -> x0])).", + "a x3", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]); [(or [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) -> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]) (not [x -> x0]))]; [[[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]] -> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] [('P : prop) -> (or 'P (not 'P))]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [x -> x0])]]) (not [x -> x0]))].", + "c em", + "=> (em goal)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 541, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0); x0.", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false].", + "intro.", + "a not_e", + "=> (not x); x.", + "a exfalso", + "=> false.", + "a x2", + "=> [x -> false]; [(not x) -> false].", + "intro.", + "a x2", + "=> [x -> false]; [(not x) -> false].", + "intro.", + "a not_e", + "=> (not [x -> false]); [x -> false].", + "c em", + "=> (em goal7).", + "c em", + "=> (em not_e@type).", + "a exfalso", + "=> false.", + "a x2", + "=> [[false -> ('P : prop) -> 'P] -> false]; [(not [false -> ('P : prop) -> 'P]) -> false].", + "intro.", + "a x5", + "=> false.", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] -> false]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]) -> false].", + "c em", + "=> (em goal15).", + "c em", + "=> (em or_ir@type).", + "intro.", + "a x2", + "=> [(or [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false])) -> false]; [(not (or [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]))) -> false].", + "a or_e", + "=> [[[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] -> [(or [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false])) -> false]]; [(not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false]) -> [(or [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false] (not [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false])) -> false]].", + "c em", + "=> (em not_i@type).", + "intro.", + "c x6", + "=> (x6 x2).", + "c em", + "=> (em em@type).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 613, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a x1", + "=> x.", + "c em", + "=> (em not_i@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B]); [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B].", + "a not_i", + "=> [[('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] -> false].", + "intro.", + "a not_e", + "=> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "c x3", + "=> (x3 x x0 x1 x2).", + "a x3", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a x3", + "=> [[x -> x0] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]]; [(not [x -> x0]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]].", + "intro.", + "intro.", + "c em", + "=> (em or_il@type).", + "c x3", + "=> (x3 x x0 x4 x2).", + "a x3", + "=> [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "c em", + "=> (em goal7).", + "c em", + "=> (em not_e@type).", + "a x5", + "=> (iff (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))).", + "c em", + "=> (em x2@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))] -> (iff (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))]) -> (iff (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a iff_i", + "=> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]; [(or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])) -> (not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)])))].", + "a x3", + "=> [[x -> x0] -> [(not (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))) -> (or [('P : prop) -> ['P -> false] -> (not 'P)] (not [('P : prop) -> ['P -> false] -> (not 'P)]))]]; [(not [x -> x0]) -> 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not_i", + "=> [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "c not_e", + "=> (not_e and_el@type x0 x).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])].", + "intro.", + "a x0", + "=> (and (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "a x1", + "=> (and [[('P : prop) -> (or 'P (not 'P))] -> false] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])).", 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-> [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> [[('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] -> x1]]].", + "intro.", + "c x6", + "=> (x6 or_ir@type iff_i@type or_ir iff_i).", + "a exfalso", + "=> .", + "c x7", + "=> (x7 and_i@type not_e@type x7 not_e).", + "a exfalso", + "=> .", + "c x7", + "=> (x7 or_e@type and_el@type or_e and_el).", + "c x6", + "=> (x6 not_i@type x2@type not_i x2).", + "c x7", + "=> (x7 em@type false em x5).", + "c x7", + "=> (x7 p3@type or_ir@type p3 or_ir).", + "c x6", + "=> (x6 and_i@type and_i@type and_i and_i)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 532, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_er@type).", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + 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-> (and 'P 'Q) -> 'Q])) -> (or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))] -> false].", + "intro.", + "c x", + "=> (x p2@type and_i@type and_i).", + "c x", + "=> (x p0@type p1@type p1).", + "a or_e", + "=> [(or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [('P : prop) -> (not 'P) -> 'P -> false]) -> false]; [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> false].", + "c em", + "=> (em goal).", + "c x0", + "=> (x0 p9@type false).", + "intro.", + "c em", + "=> (em goal8).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "c x", + "=> (x p10@type p3@type p3).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] -> false]]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 3846, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false].", + "c em", + "=> (em and_el@type).", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "c x0", + "=> (x0 and_er@type or_ir@type or_ir).", + "c x0", + "=> (x0 p@type and_el@type x).", + "a exfalso", + "=> false.", + "c x0", + "=> 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'Q)] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]]]; [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]]].", + "intro.", + "a x", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "c x0", + "=> (x0 goal20 or_e@type or_e).", + "a x", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) [('P : prop) -> (not 'P) -> 'P -> false]).", + "c x0", + "=> (x0 goal13 p1@type p1).", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false] (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> (not (and (and false [('P : prop) -> ['P -> false] -> (not 'P)]) false))]] [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]) [('P : prop) -> (not 'P) -> 'P -> false])).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 475, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [(not (and x x0)) -> (or (not x) (not x0))]); [(not (and x x0)) -> (or (not x) (not x0))].", + "a not_i", + "=> [[(not (and x x0)) -> (or (not x) (not x0))] -> false].", + "intro.", + "a not_e", + "=> (not false); false.", + "a not_i", + "=> [false -> false].", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [false -> false]].", + "a x1", + "=> (and [('P : prop) -> ['P -> false] -> (not 'P)] [[('P : prop) -> (not 'P) -> 'P -> false] -> [false -> false]]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a not_i", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> false.", + "a x1", + "=> (and [('P : 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-> false] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 405, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> (not x0).", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not x0).", + "a not_i", + "=> [x0 -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ['P -> false] -> (not 'P)]).", + "c em", + "=> (em iff_i@type).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> false].", + "c em", + "=> (em goal12).", + "a exfalso", + "=> false.", + "c em", + "=> (em x1@type).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> false].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> false]]].", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(not (and x x0)) -> false]; [(not (not (and x x0))) -> false].", + "c em", + "=> (em goal1@2).", + "a or_e", + "=> [(not (and x x0)) -> [(not (and x x0)) -> false]]; [(not (not (and x x0))) -> [(not (and x x0)) -> false]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false] -> [(not (and x x0)) -> [(not (and x x0)) -> false]]]; [(not [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]) -> [(not (and x x0)) -> [(not (and x x0)) -> false]]].", + "c em", + "=> (em goal17).", + "intro.", + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2552, + "actions": [ + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c em", + "=> (em and_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> false].", + "intro.", + "a x", + "=> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))].", + "intro.", + "a x", + "=> (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]).", + "a x0", + "=> (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]).", + "a x", + "=> (and (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c em", + "=> (em goal7).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> (and (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])].", + "intro.", + "a and_i", + "=> (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P])))]).", + "a or_e", + "=> [(and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]]) -> (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) 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-> (iff false [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)])].", + "c x1", + "=> (x1 or_e@type p@type p7 p)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 517, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em and_er@type).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not false); false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not false)]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not false)].", + "intro.", + "a not_i", + "=> [false -> false].", + "intro.", + "intro.", + "a not_i", + "=> [false -> false].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> false].", + "intro.", + "a not_e", + "=> (not [false -> ('P : prop) -> 'P]).", + "a not_i", + "=> [[false -> ('P : prop) -> 'P] -> false].", + "c em", + "=> (em 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-> ['P -> 'Q]]).", + "c em", + "=> (em or_e@type).", + "a and_i", + "=> false.", + "a x0", + "=> (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))).", + "a x0", + "=> (and (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])).", + "a x", + "=> (and (and (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a x", + "=> (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))).", + "a x0", + "=> (and (and (and (and (and false (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))) (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false] (and (and (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false]) [('P : prop) -> ['P -> false] -> (not 'P)]) (and false [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> false])))) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 336, + "actions": [ + "intro.", + "intro.", + "c em", + "=> (em iff_el@type).", + "a exfalso", + "=> 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(iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))].", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))).", + "a iff_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))]; [(iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false)) -> [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]].", + "a x2", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] false))).", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]].", + "c em", + "=> (em x).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]].", + "c em", + "=> (em goal16).", + "a x1", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]])].", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])); (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))].", + "a x3", + "=> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]))).", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]] -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]]) -> (iff [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] (not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]])))].", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 10810, + "actions": [ + "c em", + "=> (em and_i@type).", + "intro.", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x].", + "intro.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x].", + "intro.", + "c x2", + "=> (x2 or_ir@type iff_er@type or_ir iff_er).", + "c x2", + "=> (x2 and_i@type and_i@type x2 x2).", + "c and_el", + "=> (and_el or_ir@type iff_er@type p0).", + "c x1", + "=> (x1 and_er@type and_i@type and_er x1).", + "c em", + "=> (em x0@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x]; [(not [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) -> x].", + "c x1", + "=> (x1 not_i@type iff_i@type not_i iff_i).", + "c and_el", + "=> (and_el and_i@type and_i@type p1).", + "c x2", + "=> (x2 p1@type and_er@type p1 and_er).", + "c p2", + "=> (p2 goal and_i@type and_i).", + "c and_el", + "=> (and_el and_er@type and_i@type p3).", + "c em", + "=> (em p4@type@2).", + "c x2", + "=> (x2 or_il@type and_i@type or_il x2).", + "c p2", + "=> (p2 em@type or_ir@type or_ir).", + "c p9", + "=> (p9 or_il@type and_i@type p11).", + "c p9", + "=> (p9 and_i@type and_i@type p1).", + "a p9", + "=> (and false [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x]).", + "c x2", + "=> (x2 p10@type or_il@type p10 or_il).", + "a or_e", + "=> [(not [x -> (not x)]) -> (and false [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x])]; [(not (not [x -> (not x)])) -> (and false [[('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)] -> x])].", + "c p2", + "=> (p2 p10@type p12@type p12).", + "c x1", + "=> (x1 p7@type and_er@type p7 and_er).", + "c x2", + "=> (x2 p1@type p5@type p1 p5).", + "c p13", + "=> (p13 p16@type p4@type p16 p4).", + "c p9", + "=> (p9 and_er@type and_i@type p3).", + "c and_el", + "=> (and_el p7@type and_er@type p17)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 38, + "evals_used": 1718, + "actions": [ + "intro.", 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(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "c x1", + "=> (x1 em@type or_ir@type p2 or_ir).", + "c x1", + "=> (x1 and_el@type or_e@type and_el or_e).", + "c x1", + "=> (x1 not_e@type em@type not_e p2).", + "c and_er", + "=> (and_er and_el@type or_e@type p4).", + "c p2" + ] + } + ], + "problem": "extrinsic_L4_11" + }, + { + "solved": false, + "greedy_solved": false, + "n_traces": 15, + "evals_used": 41921, + "solution_actions": null, + "traces": [ + { + "mode": "greedy", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 352, + "actions": [ + "intro.", + "intro.", + "a x0", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not (not x)); (not x).", + "a not_i", + "=> [(not x) -> false].", + "intro.", + "a not_e", + "=> (not 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"=> (em iff_i@type).", + "a or_e", + "=> [[x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]] -> false]; [(not [x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]]) -> false].", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "c x6", + "=> (x6 iff_el@type).", + "a exfalso", + "=> false.", + "c em", + "=> (em iff_er@type).", + "a not_e", + "=> (not (or [x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]] (not [x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]]))).", + "a not_i", + "=> [(or [x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]] (not [x -> [x -> [x -> [x -> [[('P : prop) -> (or 'P (not 'P))] -> false]]]]])) -> false].", + "intro.", + "c x6", + "=> (x6 p2@type).", + "a not_e", + "=> (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]))))).", + "a or_e", + "=> [(or x (not x)) -> (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))]; [(not (or x (not x))) -> (not (or (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])) (not (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)])))))].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> (or 'P (not 'P))])); (not [('P : prop) -> (or 'P (not 'P))])." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 309, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('A : prop) -> [(not 'A) -> 'A] -> 'A]); [('A : prop) -> [(not 'A) -> 'A] -> 'A].", + "a not_i", + "=> [[('A : prop) -> [(not 'A) -> 'A] -> 'A] -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "c x1", + "=> (x1 x x0).", + "a x1", + "=> [(not (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) -> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])].", + "intro.", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "a x1", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]].", + "c em", + "=> (em iff_el@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "c em", + "=> (em goal10).", + "intro.", + "a x1", + "=> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]].", + "a x3", + "=> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]).", + "a x1", + "=> [(not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) -> (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])].", + "a x3", + "=> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])).", + "a x1", + "=> [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))].", + "a x1", + "=> [(not [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]) -> [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]].", + "intro.", + "a x1", + "=> [(not [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]) -> [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]].", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> [(not [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]) -> [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]]]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) -> [(not [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]) -> [(not (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))) -> (iff (not (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]])) (iff (not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]))]]].", + "a exfalso", + "=> false.", + "a or_e", + "=> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]; [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]]) -> false].", + "c em", + "=> (em and_i@type).", + "a x1", + "=> [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]].", + "a x1", + "=> [(not [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]) -> [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]].", + "a x3", + "=> (iff (not [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]) [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]).", + "a x1", + "=> [(not (iff (not [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]) [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]])) -> (iff (not [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]]) [(not [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]) -> [[[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> [(not [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]) -> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false]]] -> false]])]." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 7157, + "actions": [ + "intro.", + "intro.", + "a x0", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "c em", + "=> (em or_il@type).", + "intro.", + "a not_e", + "=> (not x).", + "a not_i", + "=> [x -> false].", + "intro.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "c em", + "=> (em not_e@type).", + "intro.", + "a exfalso", + "=> false.", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]; [(not [('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)]) -> false].", + "c x3", + "=> (x3 and_i@type and_er@type and_er).", + "c x3", + "=> (x3 iff_i@type p@type p).", + "c x3", + "=> (x3 false or_ir@type x3).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "c em", + "=> (em exfalso@type).", + "c em", + "=> (em p4@type@2).", + "intro.", + "c x3", + "=> (x3 and_el@type and_i@type and_i).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]]; [(not [('P : prop) -> (not 'P) -> 'P -> false]) -> [[('P : prop) -> ('Q : prop) -> 'P -> (or 'P 'Q)] -> false]].", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 iff_i@type iff_er@type iff_er).", + "a not_e", + "=> (not (or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P])))).", + "c x3", + "=> (x3 goal2 not_e@type x4).", + "a not_i", + "=> [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false].", + "a or_e", + "=> [[x -> false] -> [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false]]; [[('P : prop) -> (not 'P) -> 'P -> false] -> [(or (not [false -> ('P : prop) -> 'P]) (not (not [false -> ('P : prop) -> 'P]))) -> false]].", + "c x3", + "=> (x3 p5@type@2 iff_i@type iff_i).", + "c em", + "=> (em goal18).", + "c x3", + "=> (x3 p4@type p7@type p7)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 500, + "actions": [ + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> false].", + "intro.", + "c em", + "=> (em not_e@type).", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : 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false [x -> false])]; [[(not x) -> x] -> (or false [x -> false])].", + "a exfalso", + "=> false.", + "a x2", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]); [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]; [[('P : prop) -> ['P -> false] -> (not 'P)] -> false].", + "a x2", + "=> (or (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])); [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])]; [(or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]) -> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)])].", + "a or_ir", + "=> (or [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] [('P : prop) -> ['P -> false] -> (not 'P)]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [(not x) -> x])); (not [(not x) -> x]).", + "a exfalso", + "=> false.", + "a exfalso", + "=> false.", + "a or_e", + "=> [(or [('A : prop) -> [(not 'A) -> 'A] -> 'A] [('P : prop) -> ['P -> false] -> (not 'P)]) -> false]; [(not (or [('A : prop) -> [(not 'A) -> 'A] -> 'A] [('P : prop) -> ['P -> false] -> (not 'P)])) -> false].", + "c em", + "=> (em p0@type)." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 444, + "actions": [ + "c em", + "=> (em not_e@type).", + "intro.", + "intro.", + "c em", + "=> (em p@type).", + "c em", + "=> (em x).", + "a x0", + "=> (not x).", + "a or_e", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> (not x)]; [(not [('P : prop) -> (not 'P) -> 'P -> 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[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])].", + "intro.", + "a x", + "=> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]); [[('P : prop) -> ['P -> false] -> (not 'P)] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])]; [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]] -> (not [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))])].", + "a x", + "=> (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] [false -> ('P : prop) -> 'P]); [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : 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prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]; [(not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))].", + "c em", + "=> (em p@type).", + "a x", + "=> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))))); [(or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]]; [(or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))) -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))]].", + "a x", + "=> (or (or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))].", + "a or_ir", + "=> .", + "c em", + "=> (em iff_er@type).", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]]; [(not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]) -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]].", + "intro.", + "a x", + "=> (or [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))] [('P : prop) -> (or 'P (not 'P))]); [[(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]]; [[('P : prop) -> (or 'P (not 'P))] -> [(or [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]))) -> (or (or [('P : prop) -> ['P -> false] -> (not 'P)] [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['P -> 'Q]]) (or (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) (not (or [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] (not [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])))))]].", + "c em", + "=> (em iff_i@type).", + "c 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prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]].", + "c em", + "=> (em p5@type@2).", + "intro.", + "c em", + "=> (em p@type).", + "a x0", + "=> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]); [[[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]]; [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) 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prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]] -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [('B : prop) -> (or (iff x 'B) (iff x (not 'B)))]]]]] [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q])]; [(or (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) (not (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))) -> (or [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ('R 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-> false] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> (or (or x x0) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])]; [(not [('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)]) -> (or (or x x0) [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> false])].", + "c em", + "=> (em p1@type).", + "intro.", + "c em", + "=> (em x).", + "a x2", + "=> (or [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> [[('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R] -> [[('P : prop) -> ('Q : prop) -> ['P -> 'Q] -> ['Q -> 'P] -> (iff 'P 'Q)] -> false]]] [[('P : prop) -> ('Q : prop) -> ('R : 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-> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])]; [(not (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])) -> (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]))) [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R])].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] (and (and (and (and false (or [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] (not 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-> false]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]])) (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]))." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 348, + "actions": [ + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> (or (not x) (or (not x0) (not x1))).", + "a or_ir", + "=> (or (not x0) (not x1)).", + "a or_ir", + "=> (not x1).", + "a not_i", + "=> [x1 -> false].", + "intro.", + "a not_e", + "=> (not (not x0)); (not x0).", + "a not_i", + "=> [(not x0) -> false].", + "intro.", + "a not_e", + "=> (not x1).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (or (and x (and x0 x1)) (or (not x) (or (not x0) (not x1))))); (or (and x (and x0 x1)) (or (not x) (or (not x0) 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(not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)] x0) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)])) [(or x x0) -> (or x x1)]).", + "a x3", + "=> (and (and (and (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)] x0) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)])) [(or x x0) -> (or x x1)]) [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])]); [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]) -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]].", + "a or_e", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]]]; [(not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P]) -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]]].", + "intro.", + "a x3", + "=> (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])).", + "a x4", + "=> (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])) [('P : prop) -> (or 'P (not 'P))]).", + "a x3", + "=> (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]).", + "a x4", + "=> (and (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]).", + "a x5", + "=> (and (and (and (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'P] -> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])]] (not [[(or x x0) -> (or x x1)] -> (or x [x0 -> x1])])) [('P : prop) -> (or 'P (not 'P))]) [('P : prop) -> ('Q : prop) -> 'P -> 'Q -> (and 'P 'Q)]) [('P : prop) -> ('Q : prop) -> ('R : prop) -> (or 'P 'Q) -> ['P -> 'R] -> ['Q -> 'R] -> 'R]) (and (and (and (and false [('P : prop) -> (not 'P) -> 'P -> false]) [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (and (and [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)] x0) [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> (and x false)])) [(or x x0) -> (or x x1)])).", + "a exfalso" + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "max_depth", + "depth_used": 60, + "evals_used": 2279, + "actions": [ + "intro.", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (and 'P 'Q) -> 'Q] -> false].", + "intro.", + "c em", + "=> (em not_i@type).", + "a not_e", + "=> (not [('P : prop) -> (not 'P) -> 'P -> false]).", + "a not_i", + "=> [[('P : prop) -> (not 'P) -> 'P -> false] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a exfalso", + "=> false.", + "a x2", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)])); (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]).", + "c x3", + "=> (x3 goal1 p@type p).", + "a exfalso", + "=> false.", + "a x1", + "=> (and [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false] false).", + "a exfalso", + "=> false.", + "c x3", + "=> (x3 goal11 p0@type p0).", + "a or_e", + "=> [[('P : prop) -> ['P -> false] -> (not 'P)] -> false]; [(not [('P : prop) -> ['P -> false] -> (not 'P)]) -> false].", + "c em", + "=> (em goal8).", + "c em", + "=> (em or_ir@type).", + "intro.", + "c em", + "=> (em p0@type).", + "a not_e", + "=> (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]); [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false].", + "a x1", + "=> (and (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]) (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false])).", + "a and_i", + "=> (not [('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)]); (not [[('P : prop) -> ('Q : prop) -> 'Q -> (or 'P 'Q)] -> false]).", + "c x3", + "=> (x3 goal or_e@type or_e).", + "a exfalso", + "=> false." + ] + }, + { + "mode": "sample", + "temperature": 1.0, + "solved": false, + "outcome": "timeout", + "depth_used": 52, + "evals_used": 97851, + "actions": [ + "intro.", + "intro.", + "intro.", + "intro.", + "a or_ir", + "=> [x0 -> x1].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]]).", + "a not_i", + "=> [[('P : prop) -> ('Q : prop) -> (iff 'P 'Q) -> ['Q -> 'P]] -> false].", + "intro.", + "a exfalso", + "=> false.", + "a not_e", + "=> (not [('P : prop) -> (or 'P (not 'P))]).", + "a not_i", + "=> [[('P : prop) -> (or 'P (not 'P))] -> false].", + "intro.", + "c x5", + "=> (x5 goal9).", + "a not_e", + "=> (not (not (not [('P : prop) -> (or 'P (not 'P))]))); (not (not [('P : prop) -> (or 'P (not 'P))])).", + "a exfalso", + "=> false.", + "c x5", + "=> (x5 goal10).", + "c x5", + "=> (x5 x1).", + "a exfalso", + "=> false.", + "c em", + "=> (em not_e@type).", + "c x5", + "=> (x5 goal).", + "c x5", + "=> (x5 goal0).", + "a or_e", + "=> [[('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] -> false]; [(not [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]]) -> false].", + "c em", + "=> (em or_ir@type).", + "intro.", + "a exfalso", + "=> false.", + "c em", + "=> (em x).", + "c x5", + "=> (x5 goal5).", + "c x6", + "=> (x6 p2@type p7@type@2 goal10)." + ] + } + ], + "problem": "extrinsic_L6_9" + } + ] +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log new file mode 100644 index 0000000000000000000000000000000000000000..4c88c2062dbf89db1d1fb264232658dc3b72b8d5 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.log @@ -0,0 +1,917 @@ +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +[OK ] g extrinsic_L0_1 (traces=1 evals=6) +[OK ] g extrinsic_L0_2 (traces=1 evals=18) +[OK ] g extrinsic_L0_3 (traces=1 evals=14) +[OK ] g extrinsic_L0_6 (traces=1 evals=14) +[OK ] g extrinsic_L0_4 (traces=1 evals=16) +[OK ] g extrinsic_L0_11 (traces=1 evals=16) +[OK ] g extrinsic_L0_10 (traces=1 evals=9) +[OK ] g extrinsic_L0_8 (traces=1 evals=25) +[OK ] g extrinsic_L0_7 (traces=1 evals=28) +[OK ] g extrinsic_L0_13 (traces=1 evals=10) +[OK ] g extrinsic_L0_14 (traces=1 evals=26) +[OK ] - extrinsic_L0_5 (traces=2 evals=427) +[OK ] g extrinsic_L1_4 (traces=1 evals=12) +[OK ] g extrinsic_L2_1 (traces=1 evals=29) +[OK ] - extrinsic_L0_9 (traces=2 evals=637) +[OK ] g extrinsic_L2_3 (traces=1 evals=28) +[OK ] g extrinsic_L2_4 (traces=1 evals=28) +[OK ] g extrinsic_L2_5 (traces=1 evals=48) +[OK ] - extrinsic_L1_1 (traces=3 evals=1213) +[OK ] g extrinsic_L2_7 (traces=1 evals=22) +[OK ] g extrinsic_L2_8 (traces=1 evals=30) +[OK ] g extrinsic_L2_9 (traces=1 evals=70) +[OK ] g extrinsic_L2_10 (traces=1 evals=28) +[OK ] g extrinsic_L2_11 (traces=1 evals=13) +[OK ] g extrinsic_L2_12 (traces=1 evals=50) +[OK ] g extrinsic_L2_13 (traces=1 evals=128) +[OK ] - extrinsic_L1_2 (traces=3 evals=1698) +[OK ] g extrinsic_L3_1 (traces=1 evals=27) +[OK ] g extrinsic_L3_3 (traces=1 evals=26) +[OK ] g extrinsic_L3_2 (traces=1 evals=33) +[OK ] - extrinsic_L1_3 (traces=3 evals=2059) +[OK ] g extrinsic_L3_6 (traces=1 evals=42) +[OK ] - extrinsic_L2_6 (traces=3 evals=531) +[OK ] - extrinsic_L3_4 (traces=3 evals=2014) +[OK ] - extrinsic_L3_5 (traces=3 evals=1371) +[OK ] - extrinsic_L3_9 (traces=2 evals=847) + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[OK ] - extrinsic_L3_11 (traces=4 evals=1484) + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len +[OK ] - extrinsic_L3_12 (traces=7 evals=5373) +[OK ] g extrinsic_L3_13 (traces=1 evals=24) +[ ] - extrinsic_L2_2 (traces=17 evals=14116) +[ ] - extrinsic_L3_10 (traces=17 evals=14847) + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_8 (traces=17 evals=25214) +[OK ] - extrinsic_L3_14 (traces=10 evals=11037) +[OK ] - extrinsic_L3_18 (traces=3 evals=4179) +[ ] - extrinsic_L0_12 (traces=15 evals=29922) +[ ] - extrinsic_L3_7 (traces=12 evals=14847) +[ ] - extrinsic_L3_15 (traces=15 evals=36733) +[ ] - extrinsic_L3_16 (traces=7 evals=15676) +[OK ] g extrinsic_L3_23 (traces=1 evals=143) + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_17 (traces=17 evals=32413) +[ ] - extrinsic_L3_19 (traces=13 evals=17486) + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527850) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace +[ ] - extrinsic_L3_20 (traces=9 evals=18544) +[ ] - extrinsic_L3_21 (traces=17 evals=30159) + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1527850) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527850) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_22 (traces=16 evals=22238) + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_24 (traces=17 evals=27035) +[ ] - extrinsic_L3_25 (traces=11 evals=22240) +[ ] - extrinsic_L3_26 (traces=15 evals=20490) +[ ] - extrinsic_L3_28 (traces=12 evals=22633) +[ ] - extrinsic_L3_27 (traces=11 evals=19744) + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L3_29 (traces=14 evals=30536) +[ ] - extrinsic_L4_1 (traces=8 evals=11353) +[ ] - extrinsic_L4_2 (traces=17 evals=36861) + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527848) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_3 (traces=15 evals=33246) +[ ] - extrinsic_L4_5 (traces=17 evals=28129) +[ ] - extrinsic_L4_4 (traces=17 evals=21275) +[ ] - extrinsic_L4_8 (traces=17 evals=18960) +[ ] - extrinsic_L4_6 (traces=14 evals=28885) +[ ] - extrinsic_L4_9 (traces=17 evals=38104) +[ ] - extrinsic_L4_7 (traces=13 evals=27944) + +thread '' (1527852) panicked at src/universe/term.rs:851:75: +mid > len +note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace + +thread '' (1527852) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_10 (traces=10 evals=27000) +[ ] - extrinsic_L4_11 (traces=14 evals=29394) + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527852) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527849) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L4_12 (traces=15 evals=41921) +[ ] - extrinsic_L4_13 (traces=13 evals=23600) +[ ] - extrinsic_L4_14 (traces=13 evals=38761) +[ ] - extrinsic_L5_1 (traces=6 evals=16941) +[ ] - extrinsic_L5_2 (traces=7 evals=22070) +[ ] - extrinsic_L5_3 (traces=13 evals=29338) + +thread '' (1527850) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_4 (traces=3 evals=16724) +[ ] - extrinsic_L5_5 (traces=16 evals=36968) + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_7 (traces=8 evals=16318) +[OK ] g extrinsic_L6_1 (traces=1 evals=35) +[ ] - extrinsic_L5_6 (traces=14 evals=40289) + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_8 (traces=12 evals=30502) + +thread '' (1527845) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_9 (traces=5 evals=25688) + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527851) panicked at src/universe/term.rs:851:75: +mid > len + +thread '' (1527852) panicked at src/universe/term.rs:851:75: +mid > len +[ ] - extrinsic_L5_10 (traces=5 evals=7972) +[OK ] g extrinsic_L6_6 (traces=1 evals=58) +[ ] - extrinsic_L6_2 (traces=17 evals=28505) +[ ] - extrinsic_L5_11 (traces=16 evals=69497) +[ ] - extrinsic_L6_3 (traces=5 evals=29608) +[ ] - extrinsic_L6_4 (traces=2 evals=82151) +[ ] - extrinsic_L6_5 (traces=12 evals=15997) +[ ] - extrinsic_L6_8 (traces=13 evals=24999) +[ ] - extrinsic_L6_9 (traces=10 evals=108925) +[ ] - extrinsic_L6_7 (traces=6 evals=7127) +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] +L0_1 [('A : prop) -> ['A -> 'A]] +L0_2 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'A] +L0_3 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> 'B] +L0_4 [('A : prop) -> ('B : prop) -> 'A -> 'B -> (and 'A 'B)] +L0_5 [('A : prop) -> ('B : prop) -> 'A -> (or 'A 'B)] +L0_6 [('A : prop) -> ('B : prop) -> 'B -> (or 'A 'B)] +L0_7 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['A -> 'B]] +L0_8 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> ['B -> 'A]] +L0_9 [('A : prop) -> (not 'A) -> 'A -> false] +L0_10 [false -> ('A : prop) -> 'A] +L0_11 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['B -> 'A] -> (iff 'A 'B)] +L0_12 [('A : prop) -> (or 'A (not 'A))] +L0_13 [('A : prop) -> ['A -> false] -> (not 'A)] +L0_14 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A 'B) -> ['A -> 'C] -> ['B -> 'C] -> 'C] +L1_1 [('A : prop) -> 'A -> (not (not 'A))] +L1_2 [('A : prop) -> ('B : prop) -> [(not 'A) -> ['A -> 'B]]] +L1_3 [('A : prop) -> ('B : prop) -> ['A -> [(not 'A) -> 'B]]] +L1_4 [('A : prop) -> ('B : prop) -> ['B -> ['A -> 'B]]] +L2_1 [('A : prop) -> ('B : prop) -> (and 'A 'B) -> (and 'B 'A)] +L2_2 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> (or 'B 'A)] +L2_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['B -> 'C] -> ['A -> 'C]]] +L2_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [['C -> 'A] -> ['C -> 'B]]] +L2_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'C 'A) -> (and 'C 'B)]] +L2_6 [('A : prop) -> ('B : prop) -> (and (not 'A) 'A) -> 'B] +L2_7 [('A : prop) -> (iff (and 'A 'A) 'A)] +L2_8 [('A : prop) -> (iff (or 'A 'A) 'A)] +L2_9 [('A : prop) -> (iff (and 'A false) false)] +L2_10 [('A : prop) -> ('B : prop) -> 'A -> (iff 'B (and 'A 'B))] +L2_11 [('A : prop) -> (iff 'A 'A)] +L2_12 [('A : prop) -> ('B : prop) -> (iff 'A 'B) -> (iff 'B 'A)] +L2_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff 'A 'B) -> (iff 'B 'C) -> (iff 'A 'C)] +L3_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> ['B -> ['A -> 'C]]] +L3_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(and 'A 'B) -> 'C]] +L3_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> [(and 'A 'B) -> 'C] -> ['A -> ['B -> 'C]]] +L3_4 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'B) -> (not 'A)]] +L3_5 [('A : prop) -> ('B : prop) -> ['A -> (not 'B)] -> ['B -> (not 'A)]] +L3_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(and 'A 'C) -> (and 'B 'C)]] +L3_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> [(or 'A 'C) -> (or 'B 'C)]] +L3_8 [('A : prop) -> ('B : prop) -> (not (or 'A 'B)) -> (and (not 'A) (not 'B))] +L3_9 [('A : prop) -> ('B : prop) -> (and (not 'A) (not 'B)) -> (not (or 'A 'B))] +L3_10 [('A : prop) -> ('B : prop) -> (or (not 'A) (not 'B)) -> (not (and 'A 'B))] +L3_11 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'A) -> 'B]] +L3_12 [('A : prop) -> ('B : prop) -> (or 'A 'B) -> [(not 'B) -> 'A]] +L3_13 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'C] -> ['B -> 'C] -> [(or 'A 'B) -> 'C]] +L3_14 [('A : prop) -> (iff (not 'A) ['A -> false])] +L3_15 [('A : prop) -> ('B : prop) -> (iff (or 'A (and 'A 'B)) 'A)] +L3_16 [('A : prop) -> ('B : prop) -> (iff (and 'A (or 'A 'B)) 'A)] +L3_17 [('A : prop) -> (not (not (not 'A))) -> (not 'A)] +L3_18 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> ['A -> (not 'B)] -> (not 'A)] +L3_19 [('A : prop) -> ('B : prop) -> ('C : prop) -> (and 'A (or 'B 'C)) -> (or (and 'A 'B) (and 'A 'C))] +L3_20 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A 'B) (and 'A 'C)) -> (and 'A (or 'B 'C))] +L3_21 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (and 'B 'C)) -> (and (or 'A 'B) (or 'A 'C))] +L3_22 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or 'A (or 'B 'C)) -> (or (or 'A 'B) 'C)] +L3_23 [('A : prop) -> ('B : prop) -> (or (and 'A 'B) (and (not 'A) 'B)) -> 'B] +L3_24 [('A : prop) -> (iff 'A (not 'A)) -> false] +L3_25 [('A : prop) -> (not (not (or 'A (not 'A))))] +L3_26 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> ['B -> 'C]] -> [(not (not 'A)) -> [(not (not 'B)) -> (not (not 'C))]]] +L3_27 [('A : prop) -> ('B : prop) -> (not (not ['A -> 'B])) -> [(not (not 'A)) -> (not (not 'B))]] +L3_28 [('A : prop) -> ('B : prop) -> ('C : prop) -> (not (not ['A -> 'B])) -> (not (not ['B -> 'C])) -> (not (not ['A -> 'C]))] +L3_29 [('A : prop) -> ('B : prop) -> (iff (not (not (and 'A 'B))) (and (not (not 'A)) (not (not 'B))))] +L4_1 [('A : prop) -> (iff 'A (not (not 'A)))] +L4_2 [('A : prop) -> [(not (not 'A)) -> 'A]] +L4_3 [('A : prop) -> ('B : prop) -> ['A -> 'B] -> [(not 'A) -> 'B] -> 'B] +L4_4 [('A : prop) -> ('B : prop) -> [(not 'A) -> (not 'B)] -> ['B -> 'A]] +L4_5 [('A : prop) -> ('B : prop) -> [[(not 'B) -> (not 'A)] -> ['A -> 'B]]] +L4_6 [('A : prop) -> ('B : prop) -> [(not 'A) -> 'B] -> [(not 'B) -> 'A]] +L4_7 [('A : prop) -> ('B : prop) -> [(not (and 'A 'B)) -> (or (not 'A) (not 'B))]] +L4_8 [('A : prop) -> ('B : prop) -> (iff ['A -> 'B] (or (not 'A) 'B))] +L4_9 [('A : prop) -> ('B : prop) -> [['A -> 'B] -> (or (not 'A) 'B)]] +L4_10 [('A : prop) -> ('B : prop) -> (or 'A ['A -> 'B])] +L4_11 [('A : prop) -> (not ['A -> (not 'A)]) -> 'A] +L4_12 [('A : prop) -> [(not 'A) -> 'A] -> 'A] +L4_13 [('A : prop) -> ('B : prop) -> (or ['A -> 'B] ['B -> 'A])] +L4_14 [('A : prop) -> ('B : prop) -> [[['A -> 'B] -> 'A] -> 'A]] +L5_1 [('A : prop) -> ('B : prop) -> (iff (or 'A (and (not 'A) 'B)) (or 'A 'B))] +L5_2 [('A : prop) -> ('B : prop) -> (iff (and 'A (or (not 'A) 'B)) (and 'A 'B))] +L5_3 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and 'A (not 'B))) 'A)] +L5_4 [('A : prop) -> ('B : prop) -> (iff (and (or 'A 'B) (or 'A (not 'B))) 'A)] +L5_5 [('A : prop) -> ('B : prop) -> (iff (not ['A -> 'B]) (and 'A (not 'B)))] +L5_6 [('A : prop) -> ('B : prop) -> (or (iff 'A 'B) (iff 'A (not 'B)))] +L5_7 [('A : prop) -> ('B : prop) -> (iff (not (iff 'A 'B)) (iff 'A (not 'B)))] +L5_8 [('A : prop) -> ('B : prop) -> (iff (iff 'A 'B) (and (or 'A (not 'B)) (or (not 'A) 'B)))] +L5_9 [('A : prop) -> ('B : prop) -> (iff (or (and 'A 'B) (and (not 'A) (not 'B))) (iff 'A 'B))] +L5_10 [('A : prop) -> ('B : prop) -> (iff (or (and 'A (not 'B)) (and (not 'A) 'B)) (not (iff 'A 'B)))] +L5_11 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or ['A -> 'B] ['B -> 'C])] +L6_1 [('A : prop) -> ('B : prop) -> ('C : prop) -> ['A -> 'B] -> ['B -> 'C] -> ['C -> 'A] -> (iff 'A 'B)] +L6_2 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or (and 'A 'B) (and (not 'A) 'C)) (and (or 'A 'C) (or (not 'A) 'B)))] +L6_3 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (and (or 'A 'B) (or (not 'A) 'C)) (or (and 'A 'C) (and (not 'A) 'B)))] +L6_4 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (iff 'A (iff 'B 'C)) (iff (iff 'A 'B) 'C))] +L6_5 [('A : prop) -> ('B : prop) -> ('C : prop) -> (iff (or 'A (iff 'B 'C)) (iff (or 'A 'B) (or 'A 'C)))] +L6_6 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(and 'A 'C) -> (and 'B 'D)]] +L6_7 [('A : prop) -> ('B : prop) -> ('C : prop) -> ('D : prop) -> ['A -> 'B] -> ['C -> 'D] -> [(or 'A 'C) -> (or 'B 'D)]] +L6_8 [('A : prop) -> ('B : prop) -> ('C : prop) -> (or (and 'A (and 'B 'C)) (or (not 'A) (or (not 'B) (not 'C))))] +L6_9 [('A : prop) -> ('B : prop) -> ('C : prop) -> [[(or 'A 'B) -> (or 'A 'C)] -> (or 'A ['B -> 'C])]] + +Wrote /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/rollout_extrinsic-95_final.json +Solved 44/94 in 6788.0s diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/train_stats.json b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/train_stats.json new file mode 100644 index 0000000000000000000000000000000000000000..e5da628a28b338ed69e0ec87f61efd5f66f0a5df --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/train_stats.json @@ -0,0 +1,3 @@ +{ + "total_gradient_steps": 44 +} \ No newline at end of file diff --git a/experiments/learnability/train_policy_only_gold/gold_1pt/s46/train.log b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/train.log new file mode 100644 index 0000000000000000000000000000000000000000..c2d3fbf986e0189e6a48b32b154a3616abdfae36 --- /dev/null +++ b/experiments/learnability/train_policy_only_gold/gold_1pt/s46/train.log @@ -0,0 +1,40 @@ +wandb: WARNING Using a boolean value for 'reinit' is deprecated. Use 'return_previous' or 'finish_previous' instead. +wandb: Tracking run with wandb version 0.24.0 +wandb: W&B syncing is set to `offline` in this directory. Run `wandb online` or set WANDB_MODE=online to enable cloud syncing. +wandb: Run data is saved locally in /datadrive/ayush/home/minimoX/learning/wandb/offline-run-20260629_071009-ozlodttl +[2026-06-29T07:10:05.614306] Seeded RNGs with seed=46 +[2026-06-29T07:10:05.614581] Loading checkpoint from /datadrive/ayush/home/minimoX/learning/outputs/bootstrap_bs_800_para/2026-03-12_23-41-21/1.pt +[2026-06-29T07:10:09.171511] Loading examples from /datadrive/ayush/home/minimoX/learning/experiments/learnability/gold_1pt/examples_policy_only.json + 1405 training examples loaded. + +============================================================ +[2026-06-29T07:10:09.173539] Starting ablation: updates_1_epoch_2ep_bs64 (mode=epoch) + n_steps=8000, batch_size=64, lr=None + output -> /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64 +============================================================ + Dedup: 1405 -> 1405 unique examples + Epoch 1/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/epoch_1.pt + Epoch 2/2: 0%| | 0/22 [00:00 /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/epoch_2.pt + Done: 2 epoch(s), 44 total steps, 1405 unique examples (batch_size=64) +[2026-06-29T07:10:18.990287] Saved trained agent to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt + +============================================================ +[2026-06-29T07:10:18.997554] All ablations complete. +============================================================ +Summary saved to /datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/summary.json + updates_1_epoch_2ep_bs64: {'path': '/datadrive/ayush/home/minimoX/learning/experiments/learnability/train_policy_only_gold/gold_1pt/s46/2026-06-29_07-10-05/updates_1_epoch_2ep_bs64/1.pt', 'total_gradient_steps': 44}