%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET067+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 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 05:25:04 AM UTC 2025
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET067+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 04:12:24 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(tptp_fun_X_8_type, type, (
% 0.14/0.41 tptp_fun_X_8: $i)).
% 0.14/0.41 tff(tptp_fun_U_0_type, type, (
% 0.14/0.41 tptp_fun_U_0: ( $i * $i ) > $i)).
% 0.14/0.41 tff(unordered_pair_type, type, (
% 0.14/0.41 unordered_pair: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.14/0.41 tptp_fun_Y_7: $i)).
% 0.14/0.41 tff(member_type, type, (
% 0.14/0.41 member: ( $i * $i ) > $o)).
% 0.14/0.41 tff(universal_class_type, type, (
% 0.14/0.41 universal_class: $i)).
% 0.14/0.41 tff(subclass_type, type, (
% 0.14/0.41 subclass: ( $i * $i ) > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[U: $i, X: $i, Y: $i] : refl((~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> ![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (^[U: $i, X: $i, Y: $i] : trans(trans(monotonicity(rewrite((member(U, universal_class) & ((U = Y) | (U = X))) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))), rewrite((member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))))), rewrite((~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.41 tff(8,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.41 tff(11,plain,(
% 0.14/0.41 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 ((~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))) <=> (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 ((((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) <=> (((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 ((~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))) <=> (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 ((~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))) <=> (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[19, 14])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[22, 13])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (^[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))))))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (![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)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 (^[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))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(27,plain,
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.42 tff(28,plain,
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.42 tff(29,plain,
% 0.14/0.42 (^[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)))))))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(30,plain,
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.42 tff(31,plain,
% 0.14/0.42 (![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)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(32,plain,
% 0.14/0.42 (^[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))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (![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)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.42 tff(34,axiom,(![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','subclass_defn')).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.42 tff(37,plain,(
% 0.14/0.42 ![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)))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[36])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 ((~![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(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7))) | ![U: $i] : ((~member(U, unordered_pair(X!8, X!8))) | member(U, unordered_pair(X!8, Y!7))))) | (~(subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 (~((~((~subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7))) | ![U: $i] : ((~member(U, unordered_pair(X!8, X!8))) | member(U, unordered_pair(X!8, Y!7))))) | (~(subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 (((~((~subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7))) | ![U: $i] : ((~member(U, unordered_pair(X!8, X!8))) | member(U, unordered_pair(X!8, Y!7))))) | (~(subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))))) | (subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 (subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 ((~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))) <=> (~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(45,axiom,(~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pair_contains_other')).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 (~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 (~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 (~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (~![X: $i, Y: $i] : subclass(unordered_pair(X, X), unordered_pair(X, Y))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.14/0.42 tff(50,plain,(
% 0.14/0.42 ~subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7))),
% 0.14/0.42 inference(skolemize,[status(sab)],[49])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 ((~(subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))))) | subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 ((~(subclass(unordered_pair(X!8, X!8), unordered_pair(X!8, Y!7)) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))))) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[52, 43])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 (((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 (member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 ((((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) | (~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8)))),
% 0.14/0.42 inference(tautology,[status(thm)],[])).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 ((((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 (~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[57, 23])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(60,plain,
% 0.22/0.43 (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (~(((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[61, 13])).
% 0.22/0.43 tff(63,plain,
% 0.22/0.43 (((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))) | (~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[63, 53])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 ((((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))) | ((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 ((((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))) <=> member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), unordered_pair(X!8, Y!7))) | ((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 ((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[66, 62])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))) | member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[68, 58])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 ((~((~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))))) | (~member(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)), universal_class)) | (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 (~((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[70, 69, 67])).
% 0.22/0.43 tff(72,plain,
% 0.22/0.43 (((tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = Y!7) | (tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8)) | (~(tptp_fun_U_0(unordered_pair(X!8, Y!7), unordered_pair(X!8, X!8)) = X!8))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(73,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[72, 71, 60])).
% 0.22/0.43 % SZS output end Proof
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------