TSTP Solution File: SET060+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 05:05:14 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.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 01:53:33 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.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(member_type, type, (
% 0.13/0.41 member: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_X_8_type, type, (
% 0.13/0.41 tptp_fun_X_8: $i)).
% 0.13/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.41 tptp_fun_Y_7: $i)).
% 0.13/0.41 tff(universal_class_type, type, (
% 0.13/0.41 universal_class: $i)).
% 0.13/0.41 tff(complement_type, type, (
% 0.13/0.41 complement: $i > $i)).
% 0.13/0.41 tff(intersection_type, type, (
% 0.13/0.41 intersection: ( $i * $i ) > $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[X: $i, Y: $i, Z: $i] : refl((member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))) <=> (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))) <=> ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[X: $i, Y: $i, Z: $i] : rewrite((member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(6,axiom,(![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','intersection')).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.41 tff(8,plain,(
% 0.13/0.41 ![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (member(Z, X) & member(Z, Y)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[7])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 ((~![X: $i, Y: $i, Z: $i] : (member(Z, intersection(X, Y)) <=> (~((~member(Z, Y)) | (~member(Z, X)))))) | (member(Y!7, intersection(complement(X!8), X!8)) <=> (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (member(Y!7, intersection(complement(X!8), X!8)) <=> (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 ((~(~member(Y!7, intersection(complement(X!8), X!8)))) <=> member(Y!7, intersection(complement(X!8), X!8))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))) <=> (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(15,axiom,(~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','special_classes_lemma')).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : (~member(Y, intersection(complement(X), X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.41 tff(23,plain,(
% 0.13/0.41 ~(~member(Y!7, intersection(complement(X!8), X!8)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (member(Y!7, intersection(complement(X!8), X!8))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 ((~(member(Y!7, intersection(complement(X!8), X!8)) <=> (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))))) | (~member(Y!7, intersection(complement(X!8), X!8))) | (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((~(member(Y!7, intersection(complement(X!8), X!8)) <=> (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))))) | (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 12])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) | member(Y!7, X!8)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (member(Y!7, X!8)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (((~member(Y!7, universal_class)) | member(Y!7, X!8)) | (~member(Y!7, X!8))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 ((~member(Y!7, universal_class)) | member(Y!7, X!8)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (((~member(Y!7, X!8)) | (~member(Y!7, complement(X!8)))) | member(Y!7, complement(X!8))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (member(Y!7, complement(X!8))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 27])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~(member(Y!7, complement(X!8)) <=> (~((~member(Y!7, universal_class)) | member(Y!7, X!8))))) | (~member(Y!7, complement(X!8))) | (~((~member(Y!7, universal_class)) | member(Y!7, X!8)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~(member(Y!7, complement(X!8)) <=> (~((~member(Y!7, universal_class)) | member(Y!7, X!8))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[34, 33, 31])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (^[X: $i, Z: $i] : refl((member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))) <=> (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))) <=> ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[X: $i, Z: $i] : rewrite((member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X)))) <=> ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,axiom,(![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','complement')).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,(
% 0.20/0.41 ![X: $i, Z: $i] : (member(Z, complement(X)) <=> (member(Z, universal_class) & (~member(Z, X))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 ((~![X: $i, Z: $i] : (member(Z, complement(X)) <=> (~((~member(Z, universal_class)) | member(Z, X))))) | (member(Y!7, complement(X!8)) <=> (~((~member(Y!7, universal_class)) | member(Y!7, X!8))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[46, 45, 35])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------