%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET043+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:24:57 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET043+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 04:06:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(element_type, type, (
% 0.12/0.38 element: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (((~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))) | $false) <=> (~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~$true) <=> $false),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((element(X!0, X!0) <=> element(X!0, X!0)) <=> $true),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((~(element(X!0, X!0) <=> element(X!0, X!0))) <=> (~$true)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~(element(X!0, X!0) <=> element(X!0, X!0))) <=> $false),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (((~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))) | (~(element(X!0, X!0) <=> element(X!0, X!0)))) <=> ((~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))) | $false)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (((~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))) | (~(element(X!0, X!0) <=> element(X!0, X!0)))) <=> (~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))) | (~(element(X!0, X!0) <=> element(X!0, X!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[Y: $i] : refl((~(element(Y, Y) <=> element(Y, X!0))) <=> (~(element(Y, Y) <=> element(Y, X!0))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0))) <=> ![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X))) <=> ?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~(~?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X))))) <=> ?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (element(Y, X) <=> (~element(Y, Y)))) <=> (~?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ((~(~?[X: $i] : ![Y: $i] : (element(Y, X) <=> (~element(Y, Y))))) <=> (~(~?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~(~?[X: $i] : ![Y: $i] : (element(Y, X) <=> (~element(Y, Y))))) <=> ?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[15, 13])).
% 0.12/0.38 tff(17,axiom,(~(~?[X: $i] : ![Y: $i] : (element(Y, X) <=> (~element(Y, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel39')).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (?[X: $i] : ![Y: $i] : (~(element(Y, Y) <=> element(Y, X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 $oeq(![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0))), ![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0))))),
% 0.12/0.38 inference(transitivity,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![Y: $i] : (~(element(Y, Y) <=> element(Y, X!0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------