%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN412+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 05:39:00 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN412+1 : TPTP v9.0.0. Released v2.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:33:39 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (((~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))) | $false) <=> (~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~$true) <=> $false),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((f(X!0, X!0) <=> f(X!0, X!0)) <=> $true),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~(f(X!0, X!0) <=> f(X!0, X!0))) <=> (~$true)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ((~(f(X!0, X!0) <=> f(X!0, X!0))) <=> $false),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (((~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))) | (~(f(X!0, X!0) <=> f(X!0, X!0)))) <=> ((~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))) | $false)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (((~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))) | (~(f(X!0, X!0) <=> f(X!0, X!0)))) <=> (~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))) | (~(f(X!0, X!0) <=> f(X!0, X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (^[Y: $i] : refl((~(f(X!0, X!0) <=> f(X!0, Y))) <=> (~(f(X!0, X!0) <=> f(X!0, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y))) <=> ![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y))) <=> ?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~(~?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y))))) <=> ?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~?[X: $i] : ![Y: $i] : (f(X, Y) <=> (~f(X, X)))) <=> (~?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 ((~(~?[X: $i] : ![Y: $i] : (f(X, Y) <=> (~f(X, X))))) <=> (~(~?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ((~(~?[X: $i] : ![Y: $i] : (f(X, Y) <=> (~f(X, X))))) <=> ?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[15, 13])).
% 0.13/0.39 tff(17,axiom,(~(~?[X: $i] : ![Y: $i] : (f(X, Y) <=> (~f(X, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish255')).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (?[X: $i] : ![Y: $i] : (~(f(X, X) <=> f(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.13/0.39 tff(20,plain,(
% 0.13/0.39 $oeq(![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y))), ![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y))))),
% 0.13/0.39 inference(transitivity,[status(sab)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![Y: $i] : (~(f(X!0, X!0) <=> f(X!0, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------