%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET054+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 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 05:25:00 AM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET054+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 04:08:48 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(subclass_type, type, (
% 0.22/0.40 subclass: ( $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_X_7_type, type, (
% 0.22/0.40 tptp_fun_X_7: $i)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 ((~![X: $i] : subclass(X, X)) <=> (~![X: $i] : subclass(X, X))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,axiom,(~![X: $i] : subclass(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_of_subclass')).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (~![X: $i] : subclass(X, X)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (~![X: $i] : subclass(X, X)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (~![X: $i] : subclass(X, X)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (~![X: $i] : subclass(X, X)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.40 tff(7,plain,(
% 0.22/0.40 ~subclass(X!7, X!7)),
% 0.22/0.40 inference(skolemize,[status(sab)],[6])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (^[X: $i, Y: $i] : refl((~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y))) <=> (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y))) <=> ![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((subclass(X, Y) & subclass(Y, X)) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))), (((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))))), rewrite(((X = Y) <=> (~((~subclass(X, Y)) | (~subclass(Y, X))))) <=> (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))), (((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y))))), rewrite((~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y))) <=> (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))), (((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(13,axiom,(![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','extensionality')).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.40 tff(15,plain,(
% 0.22/0.40 ![X: $i, Y: $i] : ((X = Y) <=> (subclass(X, Y) & subclass(Y, X)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[14])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | subclass(X!7, X!7)) <=> ((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | subclass(X!7, X!7))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 ((~(~subclass(X!7, X!7))) <=> subclass(X!7, X!7)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (((~subclass(X!7, X!7)) <=> $true) <=> (~subclass(X!7, X!7))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 ((X!7 = X!7) <=> $true),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (~subclass(X!7, X!7))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 ((((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7)) <=> ((~subclass(X!7, X!7)) <=> $true)),
% 0.22/0.40 inference(monotonicity,[status(thm)],[22, 21])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 ((((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7)) <=> (~subclass(X!7, X!7))),
% 0.22/0.40 inference(transitivity,[status(thm)],[23, 20])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 ((~(((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7))) <=> (~(~subclass(X!7, X!7)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 ((~(((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7))) <=> subclass(X!7, X!7)),
% 0.22/0.40 inference(transitivity,[status(thm)],[25, 19])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | (~(((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7)))) <=> ((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | subclass(X!7, X!7))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[26])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 (((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | (~(((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7)))) <=> ((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | subclass(X!7, X!7))),
% 0.22/0.40 inference(transitivity,[status(thm)],[27, 18])).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 ((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | (~(((~subclass(X!7, X!7)) | (~subclass(X!7, X!7))) <=> (X!7 = X!7)))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 ((~![X: $i, Y: $i] : (~(((~subclass(X, Y)) | (~subclass(Y, X))) <=> (X = Y)))) | subclass(X!7, X!7)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[30, 17, 7])).
% 0.22/0.40 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------