%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET102+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:25:14 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 : SET102+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 04:17:33 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(unordered_pair_type, type, (
% 0.18/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.18/0.38 tff(singleton_type, type, (
% 0.18/0.38 singleton: $i > $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(tptp_fun_X_8_type, type, (
% 0.18/0.38 tptp_fun_X_8: $i)).
% 0.18/0.38 tff(ordered_pair_type, type, (
% 0.18/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.18/0.38 tff(universal_class_type, type, (
% 0.18/0.38 universal_class: $i)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 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')).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.38 tff(6,plain,(
% 0.18/0.38 ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[5])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 ((~![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))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (ordered_pair(X!8, Y!7) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))) = ordered_pair(X!8, Y!7)),
% 0.18/0.38 inference(symmetry,[status(thm)],[9])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7)) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.38 inference(symmetry,[status(thm)],[11])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 ((~member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))) <=> (~member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 ((~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))) <=> (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(15,axiom,(~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unordered_pair_member_of_ordered_pair')).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.38 tff(20,plain,(
% 0.18/0.38 ~member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))),
% 0.18/0.38 inference(skolemize,[status(sab)],[19])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (~member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (^[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))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.38 tff(29,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')).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.38 tff(32,plain,(
% 0.18/0.38 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[31])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[33, 23])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (((~![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, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(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, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ((~(~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))) <=> (member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 ((~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | $false) <=> (~member(unordered_pair(X!8, singleton(Y!7)), universal_class))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 ((~$true) <=> $false),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (($true | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))) <=> $true),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) <=> $true),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))) <=> ($true | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))) <=> $true),
% 0.18/0.38 inference(transitivity,[status(thm)],[43, 41])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 ((~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))) <=> (~$true)),
% 0.18/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 ((~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))) <=> $false),
% 0.18/0.39 inference(transitivity,[status(thm)],[45, 40])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> ((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | $false)),
% 0.18/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> (~member(unordered_pair(X!8, singleton(Y!7)), universal_class))),
% 0.18/0.39 inference(transitivity,[status(thm)],[47, 39])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))) <=> ((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 ((((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[49, 38])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))) <=> (~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[50, 37])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 ((~(((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (~(~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((~(((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))) <=> (member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[52, 36])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (((~![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, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(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, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (((~![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, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(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, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[54, 35])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 ((~![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, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 ((~![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, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[57, 34])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(62,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.39 tff(64,plain,(
% 0.18/0.39 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.18/0.39 inference(skolemize,[status(sab)],[63])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(X!8, singleton(Y!7)), universal_class)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (member(unordered_pair(X!8, singleton(Y!7)), universal_class)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 ((~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))) | (~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((~(member(unordered_pair(X!8, singleton(Y!7)), universal_class) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))) | member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[69, 58])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[70, 21])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------