TSTP Solution File: SET083+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:05:29 EDT 2022
% Result : Theorem 43.86s 28.49s
% Output : Proof 43.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 02:04:44 EDT 2022
% 0.13/0.34 % 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.
% 43.86/28.49 % SZS status Theorem
% 43.86/28.49 % SZS output start Proof
% 43.86/28.49 tff(member_type, type, (
% 43.86/28.49 member: ( $i * $i ) > $o)).
% 43.86/28.49 tff(universal_class_type, type, (
% 43.86/28.49 universal_class: $i)).
% 43.86/28.49 tff(tptp_fun_X_8_type, type, (
% 43.86/28.49 tptp_fun_X_8: $i)).
% 43.86/28.49 tff(unordered_pair_type, type, (
% 43.86/28.49 unordered_pair: ( $i * $i ) > $i)).
% 43.86/28.49 tff(tptp_fun_Y_7_type, type, (
% 43.86/28.49 tptp_fun_Y_7: $i)).
% 43.86/28.49 tff(singleton_type, type, (
% 43.86/28.49 singleton: $i > $i)).
% 43.86/28.49 tff(1,plain,
% 43.86/28.49 (^[X: $i] : refl((singleton(X) = unordered_pair(X, X)) <=> (singleton(X) = unordered_pair(X, X)))),
% 43.86/28.49 inference(bind,[status(th)],[])).
% 43.86/28.49 tff(2,plain,
% 43.86/28.49 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 43.86/28.49 inference(quant_intro,[status(thm)],[1])).
% 43.86/28.49 tff(3,plain,
% 43.86/28.49 (![X: $i] : (singleton(X) = unordered_pair(X, X)) <=> ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(4,axiom,(![X: $i] : (singleton(X) = unordered_pair(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','singleton_set_defn')).
% 43.86/28.49 tff(5,plain,
% 43.86/28.49 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 43.86/28.49 tff(6,plain,(
% 43.86/28.49 ![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 43.86/28.49 inference(skolemize,[status(sab)],[5])).
% 43.86/28.49 tff(7,plain,
% 43.86/28.49 (![X: $i] : (singleton(X) = unordered_pair(X, X))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 43.86/28.49 tff(8,plain,
% 43.86/28.49 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(Y!7) = unordered_pair(Y!7, Y!7))),
% 43.86/28.49 inference(quant_inst,[status(thm)],[])).
% 43.86/28.49 tff(9,plain,
% 43.86/28.49 (singleton(Y!7) = unordered_pair(Y!7, Y!7)),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 43.86/28.49 tff(10,plain,
% 43.86/28.49 ((~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))) <=> (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y)))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(11,plain,
% 43.86/28.49 ((~![X: $i, Y: $i] : (((singleton(X) = singleton(Y)) & member(X, universal_class)) => (X = Y))) <=> (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y)))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(12,axiom,(~![X: $i, Y: $i] : (((singleton(X) = singleton(Y)) & member(X, universal_class)) => (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','singleton_identified_by_element1')).
% 43.86/28.49 tff(13,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[12, 11])).
% 43.86/28.49 tff(14,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[13, 10])).
% 43.86/28.49 tff(15,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[14, 10])).
% 43.86/28.49 tff(16,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[15, 10])).
% 43.86/28.49 tff(17,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[16, 10])).
% 43.86/28.49 tff(18,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[17, 10])).
% 43.86/28.49 tff(19,plain,
% 43.86/28.49 (~![X: $i, Y: $i] : ((~((singleton(X) = singleton(Y)) & member(X, universal_class))) | (X = Y))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[18, 10])).
% 43.86/28.49 tff(20,plain,(
% 43.86/28.49 ~((~((singleton(X!8) = singleton(Y!7)) & member(X!8, universal_class))) | (X!8 = Y!7))),
% 43.86/28.49 inference(skolemize,[status(sab)],[19])).
% 43.86/28.49 tff(21,plain,
% 43.86/28.49 ((singleton(X!8) = singleton(Y!7)) & member(X!8, universal_class)),
% 43.86/28.49 inference(or_elim,[status(thm)],[20])).
% 43.86/28.49 tff(22,plain,
% 43.86/28.49 (singleton(X!8) = singleton(Y!7)),
% 43.86/28.49 inference(and_elim,[status(thm)],[21])).
% 43.86/28.49 tff(23,plain,
% 43.86/28.49 ((~![X: $i] : (singleton(X) = unordered_pair(X, X))) | (singleton(X!8) = unordered_pair(X!8, X!8))),
% 43.86/28.49 inference(quant_inst,[status(thm)],[])).
% 43.86/28.49 tff(24,plain,
% 43.86/28.49 (singleton(X!8) = unordered_pair(X!8, X!8)),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[23, 7])).
% 43.86/28.49 tff(25,plain,
% 43.86/28.49 (unordered_pair(X!8, X!8) = singleton(X!8)),
% 43.86/28.49 inference(symmetry,[status(thm)],[24])).
% 43.86/28.49 tff(26,plain,
% 43.86/28.49 (unordered_pair(X!8, X!8) = unordered_pair(Y!7, Y!7)),
% 43.86/28.49 inference(transitivity,[status(thm)],[25, 22, 9])).
% 43.86/28.49 tff(27,plain,
% 43.86/28.49 (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, unordered_pair(Y!7, Y!7))),
% 43.86/28.49 inference(monotonicity,[status(thm)],[26])).
% 43.86/28.49 tff(28,plain,
% 43.86/28.49 (member(X!8, unordered_pair(Y!7, Y!7)) <=> member(X!8, unordered_pair(X!8, X!8))),
% 43.86/28.49 inference(symmetry,[status(thm)],[27])).
% 43.86/28.49 tff(29,plain,
% 43.86/28.49 ((~member(X!8, unordered_pair(Y!7, Y!7))) <=> (~member(X!8, unordered_pair(X!8, X!8)))),
% 43.86/28.49 inference(monotonicity,[status(thm)],[28])).
% 43.86/28.49 tff(30,assumption,(~(member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))), introduced(assumption)).
% 43.86/28.49 tff(31,plain,
% 43.86/28.49 (^[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)))))))),
% 43.86/28.49 inference(bind,[status(th)],[])).
% 43.86/28.49 tff(32,plain,
% 43.86/28.49 (![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))))))),
% 43.86/28.49 inference(quant_intro,[status(thm)],[31])).
% 43.86/28.49 tff(33,plain,
% 43.86/28.49 (^[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)))))))),
% 43.86/28.49 inference(bind,[status(th)],[])).
% 43.86/28.49 tff(34,plain,
% 43.86/28.49 (![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))))))),
% 43.86/28.49 inference(quant_intro,[status(thm)],[33])).
% 43.86/28.49 tff(35,plain,
% 43.86/28.49 (![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))))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(36,plain,
% 43.86/28.49 (^[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)))))),
% 43.86/28.49 inference(bind,[status(th)],[])).
% 43.86/28.49 tff(37,plain,
% 43.86/28.49 (![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))))),
% 43.86/28.49 inference(quant_intro,[status(thm)],[36])).
% 43.86/28.49 tff(38,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')).
% 43.86/28.49 tff(39,plain,
% 43.86/28.49 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 43.86/28.49 tff(40,plain,
% 43.86/28.49 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[39, 35])).
% 43.86/28.49 tff(41,plain,(
% 43.86/28.49 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 43.86/28.49 inference(skolemize,[status(sab)],[40])).
% 43.86/28.49 tff(42,plain,
% 43.86/28.49 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[41, 34])).
% 43.86/28.49 tff(43,plain,
% 43.86/28.49 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[42, 32])).
% 43.86/28.49 tff(44,plain,
% 43.86/28.49 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class))))))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(45,plain,
% 43.86/28.49 ((member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = Y!7)))))) <=> (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))),
% 43.86/28.49 inference(rewrite,[status(thm)],[])).
% 43.86/28.49 tff(46,plain,
% 43.86/28.49 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = Y!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class))))))),
% 43.86/28.49 inference(monotonicity,[status(thm)],[45])).
% 43.86/28.49 tff(47,plain,
% 43.86/28.49 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = Y!7))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class))))))),
% 43.86/28.49 inference(transitivity,[status(thm)],[46, 44])).
% 43.86/28.49 tff(48,plain,
% 43.86/28.49 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = Y!7))))))),
% 43.86/28.49 inference(quant_inst,[status(thm)],[])).
% 43.86/28.49 tff(49,plain,
% 43.86/28.49 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[48, 47])).
% 43.86/28.49 tff(50,plain,
% 43.86/28.49 ($false),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[49, 43, 30])).
% 43.86/28.49 tff(51,plain,(member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class))))), inference(lemma,lemma(discharge,[]))).
% 43.86/28.49 tff(52,plain,
% 43.86/28.49 (~(X!8 = Y!7)),
% 43.86/28.49 inference(or_elim,[status(thm)],[20])).
% 43.86/28.49 tff(53,plain,
% 43.86/28.49 (((~(X!8 = Y!7)) | (~member(X!8, universal_class))) | (X!8 = Y!7)),
% 43.86/28.49 inference(tautology,[status(thm)],[])).
% 43.86/28.49 tff(54,plain,
% 43.86/28.49 ((~(X!8 = Y!7)) | (~member(X!8, universal_class))),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[53, 52])).
% 43.86/28.49 tff(55,plain,
% 43.86/28.49 ((~(member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))) | (~member(X!8, unordered_pair(Y!7, Y!7))) | (~((~(X!8 = Y!7)) | (~member(X!8, universal_class))))),
% 43.86/28.49 inference(tautology,[status(thm)],[])).
% 43.86/28.49 tff(56,plain,
% 43.86/28.49 ((~(member(X!8, unordered_pair(Y!7, Y!7)) <=> (~((~(X!8 = Y!7)) | (~member(X!8, universal_class)))))) | (~member(X!8, unordered_pair(Y!7, Y!7)))),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[55, 54])).
% 43.86/28.49 tff(57,plain,
% 43.86/28.49 (~member(X!8, unordered_pair(Y!7, Y!7))),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[56, 51])).
% 43.86/28.49 tff(58,plain,
% 43.86/28.49 (~member(X!8, unordered_pair(X!8, X!8))),
% 43.86/28.49 inference(modus_ponens,[status(thm)],[57, 29])).
% 43.86/28.49 tff(59,assumption,(member(X!8, unordered_pair(X!8, X!8))), introduced(assumption)).
% 43.86/28.49 tff(60,plain,
% 43.86/28.49 ($false),
% 43.86/28.49 inference(unit_resolution,[status(thm)],[59, 58])).
% 43.86/28.49 tff(61,plain,(~member(X!8, unordered_pair(X!8, X!8))), inference(lemma,lemma(discharge,[]))).
% 43.87/28.50 tff(62,plain,
% 43.87/28.50 (member(X!8, universal_class)),
% 43.87/28.50 inference(and_elim,[status(thm)],[21])).
% 43.87/28.50 tff(63,plain,
% 43.87/28.50 ((~(member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class))) | member(X!8, unordered_pair(X!8, X!8)) | (~member(X!8, universal_class))),
% 43.87/28.50 inference(tautology,[status(thm)],[])).
% 43.87/28.50 tff(64,plain,
% 43.87/28.50 (~(member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class))),
% 43.87/28.50 inference(unit_resolution,[status(thm)],[63, 62, 61])).
% 43.87/28.50 tff(65,plain,
% 43.87/28.50 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class)))),
% 43.87/28.50 inference(rewrite,[status(thm)],[])).
% 43.87/28.50 tff(66,plain,
% 43.87/28.50 ((member(X!8, unordered_pair(X!8, X!8)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = X!8) | (X!8 = X!8)))))) <=> (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class))),
% 43.87/28.50 inference(rewrite,[status(thm)],[])).
% 43.87/28.50 tff(67,plain,
% 43.87/28.50 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = X!8) | (X!8 = X!8))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class)))),
% 43.87/28.50 inference(monotonicity,[status(thm)],[66])).
% 43.87/28.50 tff(68,plain,
% 43.87/28.50 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = X!8) | (X!8 = X!8))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class)))),
% 43.87/28.50 inference(transitivity,[status(thm)],[67, 65])).
% 43.87/28.50 tff(69,plain,
% 43.87/28.50 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = X!8) | (X!8 = X!8))))))),
% 43.87/28.50 inference(quant_inst,[status(thm)],[])).
% 43.87/28.50 tff(70,plain,
% 43.87/28.50 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, X!8)) <=> member(X!8, universal_class))),
% 43.87/28.50 inference(modus_ponens,[status(thm)],[69, 68])).
% 43.87/28.50 tff(71,plain,
% 43.87/28.50 ($false),
% 43.87/28.50 inference(unit_resolution,[status(thm)],[70, 43, 64])).
% 43.87/28.50 % SZS output end Proof
%------------------------------------------------------------------------------