%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN392+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:58 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN392+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:32:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(p2_type, type, (
% 0.12/0.37 p2: $o)).
% 0.12/0.37 tff(p1_type, type, (
% 0.12/0.37 p1: $o)).
% 0.12/0.37 tff(1,assumption,(~p2), introduced(assumption)).
% 0.12/0.37 tff(2,assumption,(~p1), introduced(assumption)).
% 0.12/0.37 tff(3,assumption,(~(p1 | (~p2))), introduced(assumption)).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (((~(p1 | (~p2))) | (~(p2 | (~p1)))) | (p1 | (~p2))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~(p1 | (~p2))) | (~(p2 | (~p1)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 ((p1 | (~p2)) | p2),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (p2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[6, 3])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~(p1 <=> p2)) | p1 | (~p2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~(p1 <=> p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7, 2])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~(~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))) <=> (((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2))) <=> (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (((p1 <=> p2) <=> (~((~(p1 | (~p2))) | (~(p2 | (~p1)))))) <=> (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (((p2 | (~p1)) & (p1 | (~p2))) <=> (~((~(p1 | (~p2))) | (~(p2 | (~p1)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))) <=> ((p1 <=> p2) <=> (~((~(p1 | (~p2))) | (~(p2 | (~p1))))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))) <=> (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[14, 12])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))) <=> (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(transitivity,[status(thm)],[15, 11])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2))))) <=> (~(~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2))))) <=> (((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2))),
% 0.12/0.37 inference(transitivity,[status(thm)],[17, 10])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 ((~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2))))) <=> (~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((p1 <=> p2) <=> ((p2 | (~p1)) & ((~p2) | p1))) <=> ((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~((p1 <=> p2) <=> ((p2 | (~p1)) & ((~p2) | p1)))) <=> (~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~((p1 <=> p2) <=> ((p2 | (~p1)) & ((~p2) | p1)))) <=> (~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2)))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.12/0.37 tff(23,axiom,(~((p1 <=> p2) <=> ((p2 | (~p1)) & ((~p2) | p1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel14')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~((p1 <=> p2) <=> ((p2 | (~p1)) & (p1 | (~p2))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 ((~((~(p1 | (~p2))) | (~(p2 | (~p1))))) | (p1 <=> p2) | (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 ((~((~(p1 | (~p2))) | (~(p2 | (~p1))))) | (p1 <=> p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 9, 5])).
% 0.12/0.37 tff(29,plain,((p1 | (~p2)) | p1), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (p1 | (~p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 2])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~(p1 | (~p2))) | p1 | (~p2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (~p2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 30, 2])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((p2 | (~p1)) | p1),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (p2 | (~p1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 2])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~((~(p1 | (~p2))) | (~(p2 | (~p1))))) | (~(p1 | (~p2))) | (~(p2 | (~p1)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (~((~(p1 | (~p2))) | (~(p2 | (~p1))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 30, 34])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (((~(p1 | (~p2))) | (~(p2 | (~p1)))) | (~(p1 <=> p2)) | (~(((~(p1 | (~p2))) | (~(p2 | (~p1)))) <=> (p1 <=> p2)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (((~(p1 | (~p2))) | (~(p2 | (~p1)))) | (~(p1 <=> p2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 25])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (~(p1 <=> p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[38, 36])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((p1 <=> p2) | p1 | p2),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[40, 39, 32, 2])).
% 0.12/0.37 tff(42,plain,(p1), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((~(p1 <=> p2)) | (~p1) | p2),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 ((~(p1 <=> p2)) | p2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (~(p1 <=> p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[44, 1])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~(p2 | (~p1))) | p2 | (~p1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 ((~(p2 | (~p1))) | p2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[46, 42])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (~(p2 | (~p1))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[47, 1])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (((~(p1 | (~p2))) | (~(p2 | (~p1)))) | (p2 | (~p1))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~(p1 | (~p2))) | (~(p2 | (~p1)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[27, 50, 45])).
% 0.12/0.37 tff(52,plain,(p2), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 ((p1 <=> p2) | (~p1) | (~p2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 ((p1 <=> p2) | (~p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (p1 <=> p2),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[54, 52])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 ((p2 | (~p1)) | (~p2)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (p2 | (~p1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[56, 52])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 ((p1 | (~p2)) | (~p1)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 (p1 | (~p2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 ((~((~(p1 | (~p2))) | (~(p2 | (~p1))))) | (~(p2 | (~p1)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 59])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 (~((~(p1 | (~p2))) | (~(p2 | (~p1))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.12/0.37 tff(62,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[38, 61, 55])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------