%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET062+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:25:02 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET062+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.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 04:09:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(member_type, type, (
% 0.13/0.40 member: ( $i * $i ) > $o)).
% 0.13/0.40 tff(null_class_type, type, (
% 0.13/0.40 null_class: $i)).
% 0.13/0.40 tff(tptp_fun_U_0_type, type, (
% 0.13/0.40 tptp_fun_U_0: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_X_7_type, type, (
% 0.13/0.40 tptp_fun_X_7: $i)).
% 0.13/0.40 tff(subclass_type, type, (
% 0.13/0.40 subclass: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : rewrite((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))), rewrite((subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))) <=> (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))), rewrite((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : rewrite((subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.40 tff(11,axiom,(![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','subclass_defn')).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.40 tff(14,plain,(
% 0.13/0.40 ![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(null_class, X!7)) | ![U: $i] : ((~member(U, null_class)) | member(U, X!7)))) | (~(subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (~((~((~subclass(null_class, X!7)) | ![U: $i] : ((~member(U, null_class)) | member(U, X!7)))) | (~(subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (((~((~subclass(null_class, X!7)) | ![U: $i] : ((~member(U, null_class)) | member(U, X!7)))) | (~(subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)))))) | (subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((~![X: $i] : subclass(null_class, X)) <=> (~![X: $i] : subclass(null_class, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(22,axiom,(~![X: $i] : subclass(null_class, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','null_class_is_subclass')).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (~![X: $i] : subclass(null_class, X)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (~![X: $i] : subclass(null_class, X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (~![X: $i] : subclass(null_class, X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~![X: $i] : subclass(null_class, X)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.41 tff(27,plain,(
% 0.21/0.41 ~subclass(null_class, X!7)),
% 0.21/0.41 inference(skolemize,[status(sab)],[26])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 ((~(subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7))))) | subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~(subclass(null_class, X!7) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7))))) | (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~member(tptp_fun_U_0(X!7, null_class), null_class)) | member(tptp_fun_U_0(X!7, null_class), X!7)) | member(tptp_fun_U_0(X!7, null_class), null_class)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (member(tptp_fun_U_0(X!7, null_class), null_class)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (^[X: $i] : refl((~member(X, null_class)) <=> (~member(X, null_class)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(36,axiom,(![X: $i] : (~member(X, null_class))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','null_class_defn')).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![X: $i] : (~member(X, null_class))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,(
% 0.21/0.41 ![X: $i] : (~member(X, null_class))),
% 0.21/0.41 inference(skolemize,[status(sab)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![X: $i] : (~member(X, null_class))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 ((~![X: $i] : (~member(X, null_class))) | (~member(tptp_fun_U_0(X!7, null_class), null_class))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[40, 39, 32])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------