TSTP Solution File: SET073+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET073+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 05:05:23 EDT 2022
% Result : Theorem 29.16s 18.99s
% Output : Proof 29.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET073+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sat Sep 3 02:00:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 29.16/18.99 % SZS status Theorem
% 29.16/18.99 % SZS output start Proof
% 29.16/18.99 tff(member_type, type, (
% 29.16/18.99 member: ( $i * $i ) > $o)).
% 29.16/18.99 tff(unordered_pair_type, type, (
% 29.16/18.99 unordered_pair: ( $i * $i ) > $i)).
% 29.16/18.99 tff(tptp_fun_Y_7_type, type, (
% 29.16/18.99 tptp_fun_Y_7: $i)).
% 29.16/18.99 tff(tptp_fun_X_8_type, type, (
% 29.16/18.99 tptp_fun_X_8: $i)).
% 29.16/18.99 tff(null_class_type, type, (
% 29.16/18.99 null_class: $i)).
% 29.16/18.99 tff(universal_class_type, type, (
% 29.16/18.99 universal_class: $i)).
% 29.16/18.99 tff(1,plain,
% 29.16/18.99 ((~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))) <=> (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class))))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.16/18.99 tff(2,plain,
% 29.16/18.99 ((~![X: $i, Y: $i] : (member(X, universal_class) => (~(unordered_pair(X, Y) = null_class)))) <=> (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class))))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.16/18.99 tff(3,axiom,(~![X: $i, Y: $i] : (member(X, universal_class) => (~(unordered_pair(X, Y) = null_class)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary1_1')).
% 29.16/18.99 tff(4,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[3, 2])).
% 29.16/18.99 tff(5,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[4, 1])).
% 29.16/18.99 tff(6,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[5, 1])).
% 29.16/18.99 tff(7,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[6, 1])).
% 29.16/18.99 tff(8,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[7, 1])).
% 29.16/18.99 tff(9,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[8, 1])).
% 29.16/18.99 tff(10,plain,
% 29.16/18.99 (~![X: $i, Y: $i] : ((~member(X, universal_class)) | (~(unordered_pair(X, Y) = null_class)))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[9, 1])).
% 29.16/18.99 tff(11,plain,(
% 29.16/18.99 ~((~member(X!8, universal_class)) | (~(unordered_pair(X!8, Y!7) = null_class)))),
% 29.16/18.99 inference(skolemize,[status(sab)],[10])).
% 29.16/18.99 tff(12,plain,
% 29.16/18.99 (unordered_pair(X!8, Y!7) = null_class),
% 29.16/18.99 inference(or_elim,[status(thm)],[11])).
% 29.16/18.99 tff(13,plain,
% 29.16/18.99 (member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, null_class)),
% 29.16/18.99 inference(monotonicity,[status(thm)],[12])).
% 29.16/18.99 tff(14,plain,
% 29.16/18.99 (member(X!8, null_class) <=> member(X!8, unordered_pair(X!8, Y!7))),
% 29.16/18.99 inference(symmetry,[status(thm)],[13])).
% 29.16/18.99 tff(15,plain,
% 29.16/18.99 ((~member(X!8, null_class)) <=> (~member(X!8, unordered_pair(X!8, Y!7)))),
% 29.16/18.99 inference(monotonicity,[status(thm)],[14])).
% 29.16/18.99 tff(16,assumption,(member(X!8, null_class)), introduced(assumption)).
% 29.16/18.99 tff(17,plain,
% 29.16/18.99 (^[X: $i] : refl((~member(X, null_class)) <=> (~member(X, null_class)))),
% 29.16/18.99 inference(bind,[status(th)],[])).
% 29.16/18.99 tff(18,plain,
% 29.16/18.99 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 29.16/18.99 inference(quant_intro,[status(thm)],[17])).
% 29.16/18.99 tff(19,plain,
% 29.16/18.99 (![X: $i] : (~member(X, null_class)) <=> ![X: $i] : (~member(X, null_class))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.16/18.99 tff(20,axiom,(![X: $i] : (~member(X, null_class))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','null_class_defn')).
% 29.16/18.99 tff(21,plain,
% 29.16/18.99 (![X: $i] : (~member(X, null_class))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[20, 19])).
% 29.16/18.99 tff(22,plain,(
% 29.16/18.99 ![X: $i] : (~member(X, null_class))),
% 29.16/18.99 inference(skolemize,[status(sab)],[21])).
% 29.16/18.99 tff(23,plain,
% 29.16/18.99 (![X: $i] : (~member(X, null_class))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[22, 18])).
% 29.16/18.99 tff(24,plain,
% 29.16/18.99 ((~![X: $i] : (~member(X, null_class))) | (~member(X!8, null_class))),
% 29.16/18.99 inference(quant_inst,[status(thm)],[])).
% 29.16/18.99 tff(25,plain,
% 29.16/18.99 ($false),
% 29.16/18.99 inference(unit_resolution,[status(thm)],[24, 23, 16])).
% 29.16/18.99 tff(26,plain,(~member(X!8, null_class)), inference(lemma,lemma(discharge,[]))).
% 29.16/18.99 tff(27,plain,
% 29.16/18.99 (~member(X!8, unordered_pair(X!8, Y!7))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[26, 15])).
% 29.16/18.99 tff(28,plain,
% 29.16/18.99 (^[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)))))))),
% 29.16/18.99 inference(bind,[status(th)],[])).
% 29.16/18.99 tff(29,plain,
% 29.16/18.99 (![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))))))),
% 29.16/18.99 inference(quant_intro,[status(thm)],[28])).
% 29.16/18.99 tff(30,plain,
% 29.16/18.99 (^[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)))))))),
% 29.16/18.99 inference(bind,[status(th)],[])).
% 29.16/18.99 tff(31,plain,
% 29.16/18.99 (![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))))))),
% 29.16/18.99 inference(quant_intro,[status(thm)],[30])).
% 29.16/18.99 tff(32,plain,
% 29.16/18.99 (![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))))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.16/18.99 tff(33,plain,
% 29.16/18.99 (^[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)))))),
% 29.16/18.99 inference(bind,[status(th)],[])).
% 29.16/18.99 tff(34,plain,
% 29.16/18.99 (![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))))),
% 29.16/18.99 inference(quant_intro,[status(thm)],[33])).
% 29.16/18.99 tff(35,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')).
% 29.16/18.99 tff(36,plain,
% 29.16/18.99 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[35, 34])).
% 29.16/18.99 tff(37,plain,
% 29.16/18.99 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[36, 32])).
% 29.16/18.99 tff(38,plain,(
% 29.16/18.99 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 29.16/18.99 inference(skolemize,[status(sab)],[37])).
% 29.16/18.99 tff(39,plain,
% 29.16/18.99 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[38, 31])).
% 29.16/18.99 tff(40,plain,
% 29.16/18.99 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 29.16/18.99 inference(modus_ponens,[status(thm)],[39, 29])).
% 29.16/18.99 tff(41,plain,
% 29.16/18.99 (((~![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, 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(X!8, Y!7)) <=> member(X!8, universal_class)))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.16/18.99 tff(42,plain,
% 29.16/18.99 ((member(X!8, unordered_pair(X!8, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = X!8)))))) <=> (member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, universal_class))),
% 29.16/18.99 inference(rewrite,[status(thm)],[])).
% 29.21/19.00 tff(43,plain,
% 29.21/19.00 (((~![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, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (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, Y!7)) <=> member(X!8, universal_class)))),
% 29.21/19.00 inference(monotonicity,[status(thm)],[42])).
% 29.21/19.00 tff(44,plain,
% 29.21/19.00 (((~![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, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (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, Y!7)) <=> member(X!8, universal_class)))),
% 29.21/19.00 inference(transitivity,[status(thm)],[43, 41])).
% 29.21/19.00 tff(45,plain,
% 29.21/19.00 ((~![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, Y!7)) <=> (~((~member(X!8, universal_class)) | (~((X!8 = Y!7) | (X!8 = X!8))))))),
% 29.21/19.00 inference(quant_inst,[status(thm)],[])).
% 29.21/19.00 tff(46,plain,
% 29.21/19.00 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, universal_class))),
% 29.21/19.00 inference(modus_ponens,[status(thm)],[45, 44])).
% 29.21/19.00 tff(47,plain,
% 29.21/19.00 (member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, universal_class)),
% 29.21/19.00 inference(unit_resolution,[status(thm)],[46, 40])).
% 29.21/19.00 tff(48,plain,
% 29.21/19.00 (member(X!8, universal_class)),
% 29.21/19.00 inference(or_elim,[status(thm)],[11])).
% 29.21/19.00 tff(49,plain,
% 29.21/19.00 ((~(member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, universal_class))) | member(X!8, unordered_pair(X!8, Y!7)) | (~member(X!8, universal_class))),
% 29.21/19.00 inference(tautology,[status(thm)],[])).
% 29.21/19.00 tff(50,plain,
% 29.21/19.00 ((~(member(X!8, unordered_pair(X!8, Y!7)) <=> member(X!8, universal_class))) | member(X!8, unordered_pair(X!8, Y!7))),
% 29.21/19.00 inference(unit_resolution,[status(thm)],[49, 48])).
% 29.21/19.00 tff(51,plain,
% 29.21/19.00 (member(X!8, unordered_pair(X!8, Y!7))),
% 29.21/19.00 inference(unit_resolution,[status(thm)],[50, 47])).
% 29.21/19.00 tff(52,plain,
% 29.21/19.00 ($false),
% 29.21/19.00 inference(unit_resolution,[status(thm)],[51, 27])).
% 29.21/19.00 % SZS output end Proof
%------------------------------------------------------------------------------