%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET101+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 05:25:13 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 : SET101+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.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 04:18:09 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(unordered_pair_type, type, (
% 0.13/0.40 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.40 tff(singleton_type, type, (
% 0.13/0.40 singleton: $i > $i)).
% 0.13/0.40 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.40 tptp_fun_Y_7: $i)).
% 0.13/0.40 tff(tptp_fun_X_8_type, type, (
% 0.13/0.40 tptp_fun_X_8: $i)).
% 0.13/0.40 tff(ordered_pair_type, type, (
% 0.13/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.13/0.40 tff(universal_class_type, type, (
% 0.13/0.40 universal_class: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(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] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','ordered_pair_defn')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))) | (ordered_pair(X!8, Y!7) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (ordered_pair(X!8, Y!7) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))) = ordered_pair(X!8, Y!7)),
% 0.13/0.40 inference(symmetry,[status(thm)],[9])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.40 tff(16,plain,(
% 0.13/0.40 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.40 inference(skolemize,[status(sab)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(X!8) = unordered_pair(X!8, X!8))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (singleton(X!8) = unordered_pair(X!8, X!8)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (unordered_pair(X!8, X!8) = singleton(X!8)),
% 0.13/0.40 inference(symmetry,[status(thm)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))) = ordered_pair(X!8, Y!7)),
% 0.13/0.40 inference(transitivity,[status(thm)],[21, 10])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(singleton(X!8), ordered_pair(X!8, Y!7))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20, 22])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (member(singleton(X!8), ordered_pair(X!8, Y!7)) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((~member(singleton(X!8), ordered_pair(X!8, Y!7))) <=> (~member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))) <=> (~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(27,axiom,(~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','singleton_member_of_ordered_pair')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (~![X: $i, Y: $i] : member(singleton(X), ordered_pair(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.40 tff(32,plain,(
% 0.13/0.40 ~member(singleton(X!8), ordered_pair(X!8, Y!7))),
% 0.13/0.40 inference(skolemize,[status(sab)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (~member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (^[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))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,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')).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.40 tff(44,plain,(
% 0.13/0.40 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 ((~(~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))) <=> (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 ((~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (((~member(unordered_pair(X!8, X!8), universal_class)) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (((~member(unordered_pair(X!8, X!8), universal_class)) | $false) <=> (~member(unordered_pair(X!8, X!8), universal_class))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 ((~$true) <=> $false),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | $true) <=> $true),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8)) <=> $true),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))) <=> ((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | $true)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[54])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))) <=> $true),
% 0.13/0.41 inference(transitivity,[status(thm)],[55, 53])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 ((~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8)))) <=> (~$true)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 ((~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8)))) <=> $false),
% 0.13/0.41 inference(transitivity,[status(thm)],[57, 52])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> ((~member(unordered_pair(X!8, X!8), universal_class)) | $false)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> (~member(unordered_pair(X!8, X!8), universal_class))),
% 0.13/0.41 inference(transitivity,[status(thm)],[59, 51])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))) <=> ((~member(unordered_pair(X!8, X!8), universal_class)) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[60])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ((((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[61, 50])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[62, 49])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 ((~(((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (~(~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~(((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[64, 48])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[66, 47])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(unordered_pair(X!8, X!8), universal_class)) | (~((unordered_pair(X!8, X!8) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, X!8) = unordered_pair(X!8, X!8))))) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 46])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(74,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.42 tff(76,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.42 inference(skolemize,[status(sab)],[75])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(X!8, X!8), universal_class)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (member(unordered_pair(X!8, X!8), universal_class)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 ((~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) | (~member(unordered_pair(X!8, X!8), universal_class)) | member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 ((~(member(unordered_pair(X!8, X!8), universal_class) <=> member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7)))))) | member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (member(unordered_pair(X!8, X!8), unordered_pair(unordered_pair(X!8, X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[81, 70])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[82, 33])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------