%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET060+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:25:01 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET060+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:09:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(member_type, type, (
% 0.18/0.38 member: ( $i * $i ) > $o)).
% 0.18/0.38 tff(complement_type, type, (
% 0.18/0.38 complement: $i > $i)).
% 0.18/0.38 tff(tptp_fun_X_8_type, type, (
% 0.18/0.38 tptp_fun_X_8: $i)).
% 0.18/0.38 tff(tptp_fun_Y_7_type, type, (
% 0.18/0.38 tptp_fun_Y_7: $i)).
% 0.18/0.38 tff(universal_class_type, type, (
% 0.18/0.38 universal_class: $i)).
% 0.18/0.38 tff(intersection_type, type, (
% 0.18/0.38 intersection: ( $i * $i ) > $i)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[X: $i, Y: $i, Z: $i] : refl((~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y)))) <=> (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (^[X: $i, Y: $i, Z: $i] : trans(trans(monotonicity(rewrite((member(Z, X) & member(Z, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))), ((member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))))), rewrite((member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))) <=> (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))), ((member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y)))))), rewrite((~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y)))) <=> (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))), ((member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(6,axiom,(![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','intersection')).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.38 tff(8,plain,(
% 0.18/0.38 ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[7])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (~(((~member(Z, Y)) | (~member(Z, X))) <=> member(Z, intersection(X, Y))))) | (~(((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) <=> member(Y!7, intersection(complement(X!8), X!8))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (~(((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) <=> member(Y!7, intersection(complement(X!8), X!8)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))) <=> (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(14,axiom,(~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','special_classes_lemma')).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.39 tff(19,plain,(
% 0.18/0.39 member(Y!7, intersection(complement(X!8), X!8))),
% 0.18/0.39 inference(skolemize,[status(sab)],[18])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 ((((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) <=> member(Y!7, intersection(complement(X!8), X!8))) | (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))) | (~member(Y!7, intersection(complement(X!8), X!8)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ((((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) <=> member(Y!7, intersection(complement(X!8), X!8))) | (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[21, 12])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) | member(Y!7, X!8)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (member(Y!7, X!8)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (((~member(Y!7, universal_class)) | member(Y!7, X!8)) | (~member(Y!7, X!8))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 ((~member(Y!7, universal_class)) | member(Y!7, X!8)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) | member(Y!7, complement(X!8))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (member(Y!7, complement(X!8))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[27, 22])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 ((((~member(Y!7, universal_class)) | member(Y!7, X!8)) <=> member(Y!7, complement(X!8))) | (~((~member(Y!7, universal_class)) | member(Y!7, X!8))) | (~member(Y!7, complement(X!8)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (((~member(Y!7, universal_class)) | member(Y!7, X!8)) <=> member(Y!7, complement(X!8))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[29, 28, 26])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (^[X: $i, Z: $i] : refl((~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X)))) <=> (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X)))) <=> ![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (^[X: $i, Z: $i] : trans(trans(monotonicity(rewrite((member(Z, universal_class) & (~member(Z, X))) <=> (~((~member(Z, universal_class)) | member(Z, X)))), ((member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))))), rewrite((member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))) <=> (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))), ((member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X)))))), rewrite((~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X)))) <=> (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))), ((member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> ![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(36,axiom,(![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','complement')).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.39 tff(38,plain,(
% 0.18/0.39 ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[37])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 ((~![X: $i, Z: $i] : (~(((~member(Z, universal_class)) | member(Z, X)) <=> member(Z, complement(X))))) | (~(((~member(Y!7, universal_class)) | member(Y!7, X!8)) <=> member(Y!7, complement(X!8))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[41, 40, 30])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------