TSTP Solution File: SET071+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET071+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 20 05:05:22 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET071+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n020.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 : Sat Sep 3 02:02:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(member_type, type, (
% 0.20/0.46 member: ( $i * $i ) > $o)).
% 0.20/0.46 tff(universal_class_type, type, (
% 0.20/0.46 universal_class: $i)).
% 0.20/0.46 tff(tptp_fun_X_8_type, type, (
% 0.20/0.46 tptp_fun_X_8: $i)).
% 0.20/0.46 tff(apply_type, type, (
% 0.20/0.46 apply: ( $i * $i ) > $i)).
% 0.20/0.46 tff(unordered_pair_type, type, (
% 0.20/0.46 unordered_pair: ( $i * $i ) > $i)).
% 0.20/0.46 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.46 tptp_fun_Y_7: $i)).
% 0.20/0.46 tff(tptp_fun_XF_6_type, type, (
% 0.20/0.46 tptp_fun_XF_6: $i)).
% 0.20/0.46 tff(null_class_type, type, (
% 0.20/0.46 null_class: $i)).
% 0.20/0.46 tff(function_type, type, (
% 0.20/0.46 function: $i > $o)).
% 0.20/0.46 tff(1,assumption,(apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7), introduced(assumption)).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (Y!7 = apply(XF!6, unordered_pair(X!8, Y!7))),
% 0.20/0.46 inference(symmetry,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (member(Y!7, universal_class) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class) <=> member(Y!7, universal_class)),
% 0.20/0.46 inference(symmetry,[status(thm)],[3])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (^[U: $i, X: $i, Y: $i] : refl((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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (^[U: $i, X: $i, Y: $i] : rewrite((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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(8,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.46 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')).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.46 tff(15,plain,(
% 0.20/0.46 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[14])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.47 tff(25,plain,(
% 0.20/0.47 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.20/0.47 inference(skolemize,[status(sab)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(X!8, Y!7), universal_class)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (member(unordered_pair(X!8, Y!7), universal_class)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 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')).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~![X: $i, Y: $i] : ((~((~member(X, universal_class)) & (~member(Y, universal_class)))) | (unordered_pair(X, Y) = null_class))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.20/0.47 tff(39,plain,(
% 0.20/0.47 ~((~((~member(X!8, universal_class)) & (~member(Y!7, universal_class)))) | (unordered_pair(X!8, Y!7) = null_class))),
% 0.20/0.47 inference(skolemize,[status(sab)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (~(unordered_pair(X!8, Y!7) = null_class)),
% 0.20/0.47 inference(or_elim,[status(thm)],[39])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (?[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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (?[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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.47 tff(47,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')).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (?[XF: $i] : (function(XF) & ![Y: $i] : (member(apply(XF, Y), Y) | (Y = null_class) | (~member(Y, universal_class))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (function(XF!6) & ![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.20/0.47 inference(and_elim,[status(thm)],[50])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![Y: $i] : ((Y = null_class) | (~member(Y, universal_class)) | member(apply(XF!6, Y), Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 ((~![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))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (member(apply(XF!6, unordered_pair(X!8, Y!7)), unordered_pair(X!8, Y!7))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[55, 52, 40, 28])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 ((~(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))) | (~((~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)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 ((~(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)), universal_class)) | (~((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (~((~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))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[58, 19])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (((~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)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (member(Y!7, universal_class)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[61, 4])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 ((~member(X!8, universal_class)) & (~member(Y!7, universal_class))),
% 0.20/0.47 inference(or_elim,[status(thm)],[39])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (~member(Y!7, universal_class)),
% 0.20/0.47 inference(and_elim,[status(thm)],[63])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.20/0.47 tff(66,plain,(~(apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (((~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))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 ((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[67, 59])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ((~((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)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 ((apply(XF!6, unordered_pair(X!8, Y!7)) = Y!7) | (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (apply(XF!6, unordered_pair(X!8, Y!7)) = X!8),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[70, 66])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (X!8 = apply(XF!6, unordered_pair(X!8, Y!7))),
% 0.20/0.48 inference(symmetry,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (member(X!8, universal_class) <=> member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (member(apply(XF!6, unordered_pair(X!8, Y!7)), universal_class) <=> member(X!8, universal_class)),
% 0.20/0.48 inference(symmetry,[status(thm)],[73])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (member(X!8, universal_class)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 74])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (~member(X!8, universal_class)),
% 0.20/0.48 inference(and_elim,[status(thm)],[63])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------