%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET071+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:25:05 AM UTC 2025
% Result : Theorem 0.44s 0.60s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET071+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:12:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.44/0.60 % SZS status Theorem
% 0.44/0.60 % SZS output start Proof
% 0.44/0.60 tff(member_type, type, (
% 0.44/0.60 member: ( $i * $i ) > $o)).
% 0.44/0.60 tff(universal_class_type, type, (
% 0.44/0.60 universal_class: $i)).
% 0.44/0.60 tff(tptp_fun_X_8_type, type, (
% 0.44/0.60 tptp_fun_X_8: $i)).
% 0.44/0.60 tff(apply_type, type, (
% 0.44/0.60 apply: ( $i * $i ) > $i)).
% 0.44/0.60 tff(unordered_pair_type, type, (
% 0.44/0.60 unordered_pair: ( $i * $i ) > $i)).
% 0.44/0.60 tff(tptp_fun_Y_7_type, type, (
% 0.44/0.60 tptp_fun_Y_7: $i)).
% 0.44/0.60 tff(tptp_fun_XF_6_type, type, (
% 0.44/0.60 tptp_fun_XF_6: $i)).
% 0.44/0.60 tff(null_class_type, type, (
% 0.44/0.60 null_class: $i)).
% 0.44/0.60 tff(function_type, type, (
% 0.44/0.60 function: $i > $o)).
% 0.44/0.60 tff(1,assumption,(apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7), introduced(assumption)).
% 0.44/0.60 tff(2,plain,
% 0.44/0.60 (Y!7 = apply(XF!6, unordered_pair(X!8, Y!7))),
% 0.44/0.60 inference(symmetry,[status(thm)],[1])).
% 0.44/0.60 tff(3,plain,
% 0.44/0.60 (member(Y!7, universal_class) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[2])).
% 0.44/0.60 tff(4,plain,
% 0.44/0.60 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class) <=> member(Y!7, universal_class)),
% 0.44/0.60 inference(symmetry,[status(thm)],[3])).
% 0.44/0.60 tff(5,plain,
% 0.44/0.60 (^[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)))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(6,plain,
% 0.44/0.60 (![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))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[5])).
% 0.44/0.60 tff(7,plain,
% 0.44/0.60 (^[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))))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(8,plain,
% 0.44/0.60 (![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))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[7])).
% 0.44/0.60 tff(9,plain,
% 0.44/0.60 (![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))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(10,plain,
% 0.44/0.60 (^[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)))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(11,plain,
% 0.44/0.60 (![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))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[10])).
% 0.44/0.60 tff(12,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.44/0.61 tff(13,plain,
% 0.44/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.44/0.61 tff(14,plain,
% 0.44/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.44/0.61 tff(15,plain,(
% 0.44/0.61 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.44/0.61 inference(skolemize,[status(sab)],[14])).
% 0.44/0.61 tff(16,plain,
% 0.44/0.61 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.44/0.61 tff(17,plain,
% 0.44/0.61 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.44/0.61 tff(18,plain,
% 0.44/0.61 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(19,plain,
% 0.44/0.61 (~(((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7)))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.44/0.61 tff(20,plain,
% 0.44/0.61 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(21,plain,
% 0.44/0.61 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.44/0.61 inference(quant_intro,[status(thm)],[20])).
% 0.44/0.61 tff(22,plain,
% 0.44/0.61 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(23,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.44/0.61 tff(24,plain,
% 0.44/0.61 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.44/0.61 tff(25,plain,(
% 0.44/0.61 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.44/0.61 inference(skolemize,[status(sab)],[24])).
% 0.44/0.61 tff(26,plain,
% 0.44/0.61 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.44/0.61 tff(27,plain,
% 0.44/0.61 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(X!8, Y!7), universal_class)),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(28,plain,
% 0.44/0.61 (member(unordered_pair(X!8, Y!7), universal_class)),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.44/0.61 tff(29,plain,
% 0.44/0.61 ((~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))) <=> (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(30,plain,
% 0.44/0.61 ((~![X: $i, Y: $i] : (((~member(X, universal_class)) & (~member(Y, universal_class))) => (unordered_pair(X, Y) = null_class))) <=> (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(31,axiom,(~![X: $i, Y: $i] : (((~member(X, universal_class)) & (~member(Y, universal_class))) => (unordered_pair(X, Y) = null_class))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','null_unordered_pair')).
% 0.44/0.61 tff(32,plain,
% 0.44/0.61 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.44/0.61 tff(33,plain,
% 0.44/0.61 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.44/0.61 tff(34,plain,
% 0.44/0.61 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.44/0.61 tff(35,plain,
% 0.44/0.61 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.44/0.61 tff(36,plain,(
% 0.44/0.61 ~((~((~member(X!8, universal_class)) & (~member(Y!7, universal_class)))) | (unordered_pair(X!8, Y!7) = null_class))),
% 0.44/0.61 inference(skolemize,[status(sab)],[35])).
% 0.44/0.61 tff(37,plain,
% 0.44/0.61 (~(unordered_pair(X!8, Y!7) = null_class)),
% 0.44/0.61 inference(or_elim,[status(thm)],[36])).
% 0.44/0.61 tff(38,plain,
% 0.44/0.61 (^[Y: $i] : refl(((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y)) <=> ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y)))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(39,plain,
% 0.44/0.61 (![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y)) <=> ![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[38])).
% 0.44/0.61 tff(40,plain,
% 0.44/0.61 ((function(XF!6) & ![Y: $i] : (member(apply(XF!6, Y), Y) | (Y = null_class) | (~member(Y, universal_class)))) <=> (function(XF!6) & ![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(41,plain,
% 0.44/0.61 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class)))) <=> ?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(42,plain,
% 0.44/0.61 (^[XF: $i] : rewrite((function(XF) & ![Y: $i] : (member(Y, universal_class) => ((Y = null_class) | member(apply(XF, Y), Y)))) <=> (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class)))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(43,plain,
% 0.44/0.61 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(Y, universal_class) => ((Y = null_class) | member(apply(XF, Y), Y)))) <=> ?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[42])).
% 0.44/0.61 tff(44,axiom,(?[XF: $i] : (function(XF) & ![Y: $i] : (member(Y, universal_class) => ((Y = null_class) | member(apply(XF, Y), Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','choice')).
% 0.44/0.61 tff(45,plain,
% 0.44/0.61 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.44/0.61 tff(46,plain,
% 0.44/0.61 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.44/0.61 tff(47,plain,
% 0.44/0.61 (function(XF!6) & ![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.44/0.61 tff(48,plain,
% 0.44/0.61 (![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.44/0.61 inference(and_elim,[status(thm)],[47])).
% 0.44/0.61 tff(49,plain,
% 0.44/0.61 (![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[48, 39])).
% 0.44/0.61 tff(50,plain,
% 0.44/0.61 (((~![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))) | ((unordered_pair(X!8, Y!7) = null_class) | (~member(unordered_pair(X!8, Y!7), universal_class)) | member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7)))) <=> ((~![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))) | (unordered_pair(X!8, Y!7) = null_class) | (~member(unordered_pair(X!8, Y!7), universal_class)) | member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(51,plain,
% 0.44/0.61 ((~![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))) | ((unordered_pair(X!8, Y!7) = null_class) | (~member(unordered_pair(X!8, Y!7), universal_class)) | member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7)))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(52,plain,
% 0.44/0.61 ((~![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))) | (unordered_pair(X!8, Y!7) = null_class) | (~member(unordered_pair(X!8, Y!7), universal_class)) | member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.44/0.61 tff(53,plain,
% 0.44/0.61 (member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[52, 49, 37, 28])).
% 0.44/0.61 tff(54,plain,
% 0.44/0.61 ((((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))) | (~((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8))))) | (~member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7)))),
% 0.44/0.61 inference(tautology,[status(thm)],[])).
% 0.44/0.61 tff(55,plain,
% 0.44/0.61 ((((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))) | (~((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.44/0.61 tff(56,plain,
% 0.44/0.61 (~((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[55, 19])).
% 0.44/0.61 tff(57,plain,
% 0.44/0.61 (((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) | member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.44/0.61 inference(tautology,[status(thm)],[])).
% 0.44/0.61 tff(58,plain,
% 0.44/0.61 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.44/0.61 tff(59,plain,
% 0.44/0.61 (member(Y!7, universal_class)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[58, 4])).
% 0.44/0.61 tff(60,plain,
% 0.44/0.61 ((~member(X!8, universal_class)) & (~member(Y!7, universal_class))),
% 0.44/0.61 inference(or_elim,[status(thm)],[36])).
% 0.44/0.61 tff(61,plain,
% 0.44/0.61 (~member(Y!7, universal_class)),
% 0.44/0.61 inference(and_elim,[status(thm)],[60])).
% 0.44/0.61 tff(62,plain,
% 0.44/0.61 ($false),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[61, 59])).
% 0.44/0.61 tff(63,plain,(~(apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.61 tff(64,plain,
% 0.44/0.61 (((~member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))) | ((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8))),
% 0.44/0.61 inference(tautology,[status(thm)],[])).
% 0.44/0.61 tff(65,plain,
% 0.44/0.61 ((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[64, 56])).
% 0.44/0.61 tff(66,plain,
% 0.44/0.61 ((~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8))) | (apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)),
% 0.44/0.61 inference(tautology,[status(thm)],[])).
% 0.44/0.61 tff(67,plain,
% 0.44/0.61 ((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.44/0.61 tff(68,plain,
% 0.44/0.61 (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[67, 63])).
% 0.44/0.61 tff(69,plain,
% 0.44/0.61 (X!8 = apply(XF!6, unordered_pair(X!8, Y!7))),
% 0.44/0.61 inference(symmetry,[status(thm)],[68])).
% 0.44/0.61 tff(70,plain,
% 0.44/0.61 (member(X!8, universal_class) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.44/0.61 inference(monotonicity,[status(thm)],[69])).
% 0.44/0.61 tff(71,plain,
% 0.44/0.61 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class) <=> member(X!8, universal_class)),
% 0.44/0.61 inference(symmetry,[status(thm)],[70])).
% 0.44/0.61 tff(72,plain,
% 0.44/0.61 (member(X!8, universal_class)),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[58, 71])).
% 0.44/0.61 tff(73,plain,
% 0.44/0.61 (~member(X!8, universal_class)),
% 0.44/0.61 inference(and_elim,[status(thm)],[60])).
% 0.44/0.61 tff(74,plain,
% 0.44/0.61 ($false),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.44/0.61 % SZS output end Proof
% 0.44/0.62 % E exiting
%------------------------------------------------------------------------------