TSTP Solution File: SET046-5 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET046-5 : TPTP v8.1.0. Released v1.0.0.
% 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 05:05:08 EDT 2022
% Result : Unsatisfiable 0.10s 0.35s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET046-5 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n021.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Sep 3 01:44:29 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.10/0.35 % SZS status Unsatisfiable
% 0.10/0.35 % SZS output start Proof
% 0.10/0.35 tff(element_type, type, (
% 0.10/0.35 element: ( $i * $i ) > $o)).
% 0.10/0.35 tff(a_type, type, (
% 0.10/0.35 a: $i)).
% 0.10/0.35 tff(f_type, type, (
% 0.10/0.35 f: $i > $i)).
% 0.10/0.35 tff(1,assumption,(~element(a, a)), introduced(assumption)).
% 0.10/0.35 tff(2,plain,
% 0.10/0.35 (^[X: $i] : refl((element(f(X), X) | element(X, a)) <=> (element(f(X), X) | element(X, a)))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(3,plain,
% 0.10/0.35 (![X: $i] : (element(f(X), X) | element(X, a)) <=> ![X: $i] : (element(f(X), X) | element(X, a))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.10/0.35 tff(4,plain,
% 0.10/0.35 (![X: $i] : (element(f(X), X) | element(X, a)) <=> ![X: $i] : (element(f(X), X) | element(X, a))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(5,axiom,(![X: $i] : (element(f(X), X) | element(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.10/0.35 tff(6,plain,
% 0.10/0.35 (![X: $i] : (element(f(X), X) | element(X, a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.10/0.35 tff(7,plain,(
% 0.10/0.35 ![X: $i] : (element(f(X), X) | element(X, a))),
% 0.10/0.35 inference(skolemize,[status(sab)],[6])).
% 0.10/0.35 tff(8,plain,
% 0.10/0.35 (![X: $i] : (element(f(X), X) | element(X, a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.10/0.35 tff(9,plain,
% 0.10/0.35 (((~![X: $i] : (element(f(X), X) | element(X, a))) | (element(a, a) | element(f(a), a))) <=> ((~![X: $i] : (element(f(X), X) | element(X, a))) | element(a, a) | element(f(a), a))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(10,plain,
% 0.10/0.35 ((element(f(a), a) | element(a, a)) <=> (element(a, a) | element(f(a), a))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(11,plain,
% 0.10/0.35 (((~![X: $i] : (element(f(X), X) | element(X, a))) | (element(f(a), a) | element(a, a))) <=> ((~![X: $i] : (element(f(X), X) | element(X, a))) | (element(a, a) | element(f(a), a)))),
% 0.10/0.35 inference(monotonicity,[status(thm)],[10])).
% 0.10/0.35 tff(12,plain,
% 0.10/0.35 (((~![X: $i] : (element(f(X), X) | element(X, a))) | (element(f(a), a) | element(a, a))) <=> ((~![X: $i] : (element(f(X), X) | element(X, a))) | element(a, a) | element(f(a), a))),
% 0.10/0.35 inference(transitivity,[status(thm)],[11, 9])).
% 0.10/0.35 tff(13,plain,
% 0.10/0.35 ((~![X: $i] : (element(f(X), X) | element(X, a))) | (element(f(a), a) | element(a, a))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(14,plain,
% 0.10/0.35 ((~![X: $i] : (element(f(X), X) | element(X, a))) | element(a, a) | element(f(a), a)),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.10/0.35 tff(15,plain,
% 0.10/0.35 (element(a, a) | element(f(a), a)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[14, 8])).
% 0.10/0.35 tff(16,plain,
% 0.10/0.35 (element(f(a), a)),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.10/0.35 tff(17,plain,
% 0.10/0.35 (^[X: $i] : refl((element(X, f(X)) | element(X, a)) <=> (element(X, f(X)) | element(X, a)))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(18,plain,
% 0.10/0.35 (![X: $i] : (element(X, f(X)) | element(X, a)) <=> ![X: $i] : (element(X, f(X)) | element(X, a))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[17])).
% 0.10/0.35 tff(19,plain,
% 0.10/0.35 (![X: $i] : (element(X, f(X)) | element(X, a)) <=> ![X: $i] : (element(X, f(X)) | element(X, a))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(20,axiom,(![X: $i] : (element(X, f(X)) | element(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.10/0.35 tff(21,plain,
% 0.10/0.35 (![X: $i] : (element(X, f(X)) | element(X, a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.10/0.35 tff(22,plain,(
% 0.10/0.35 ![X: $i] : (element(X, f(X)) | element(X, a))),
% 0.10/0.35 inference(skolemize,[status(sab)],[21])).
% 0.10/0.35 tff(23,plain,
% 0.10/0.35 (![X: $i] : (element(X, f(X)) | element(X, a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.10/0.35 tff(24,plain,
% 0.10/0.35 (((~![X: $i] : (element(X, f(X)) | element(X, a))) | (element(a, a) | element(a, f(a)))) <=> ((~![X: $i] : (element(X, f(X)) | element(X, a))) | element(a, a) | element(a, f(a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(25,plain,
% 0.10/0.35 ((element(a, f(a)) | element(a, a)) <=> (element(a, a) | element(a, f(a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(26,plain,
% 0.10/0.35 (((~![X: $i] : (element(X, f(X)) | element(X, a))) | (element(a, f(a)) | element(a, a))) <=> ((~![X: $i] : (element(X, f(X)) | element(X, a))) | (element(a, a) | element(a, f(a))))),
% 0.10/0.35 inference(monotonicity,[status(thm)],[25])).
% 0.10/0.35 tff(27,plain,
% 0.10/0.35 (((~![X: $i] : (element(X, f(X)) | element(X, a))) | (element(a, f(a)) | element(a, a))) <=> ((~![X: $i] : (element(X, f(X)) | element(X, a))) | element(a, a) | element(a, f(a)))),
% 0.10/0.35 inference(transitivity,[status(thm)],[26, 24])).
% 0.10/0.35 tff(28,plain,
% 0.10/0.35 ((~![X: $i] : (element(X, f(X)) | element(X, a))) | (element(a, f(a)) | element(a, a))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(29,plain,
% 0.10/0.35 ((~![X: $i] : (element(X, f(X)) | element(X, a))) | element(a, a) | element(a, f(a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.10/0.35 tff(30,plain,
% 0.10/0.35 (element(a, a) | element(a, f(a))),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.10/0.35 tff(31,plain,
% 0.10/0.35 (element(a, f(a))),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.10/0.35 tff(32,plain,
% 0.10/0.35 (^[Y: $i, X: $i] : refl(((~element(Y, X)) | (~element(X, Y)) | (~element(X, a))) <=> ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(33,plain,
% 0.10/0.35 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[32])).
% 0.10/0.35 tff(34,plain,
% 0.10/0.35 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(35,plain,
% 0.10/0.35 (^[Y: $i, X: $i] : rewrite((((~element(X, a)) | (~element(X, Y))) | (~element(Y, X))) <=> ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a))))),
% 0.10/0.35 inference(bind,[status(th)],[])).
% 0.10/0.35 tff(36,plain,
% 0.10/0.35 (![Y: $i, X: $i] : (((~element(X, a)) | (~element(X, Y))) | (~element(Y, X))) <=> ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(quant_intro,[status(thm)],[35])).
% 0.10/0.35 tff(37,axiom,(![Y: $i, X: $i] : (((~element(X, a)) | (~element(X, Y))) | (~element(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.10/0.35 tff(38,plain,
% 0.10/0.35 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.10/0.35 tff(39,plain,
% 0.10/0.35 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.10/0.35 tff(40,plain,(
% 0.10/0.35 ![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(skolemize,[status(sab)],[39])).
% 0.10/0.35 tff(41,plain,
% 0.10/0.35 (![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.10/0.35 tff(42,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, f(a))) | (~element(f(a), a)))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, f(a))) | (~element(f(a), a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(43,plain,
% 0.10/0.35 (((~element(a, f(a))) | (~element(f(a), a)) | (~element(f(a), a))) <=> ((~element(a, f(a))) | (~element(f(a), a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(44,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, f(a))) | (~element(f(a), a)) | (~element(f(a), a)))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, f(a))) | (~element(f(a), a))))),
% 0.10/0.35 inference(monotonicity,[status(thm)],[43])).
% 0.10/0.35 tff(45,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, f(a))) | (~element(f(a), a)) | (~element(f(a), a)))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, f(a))) | (~element(f(a), a)))),
% 0.10/0.35 inference(transitivity,[status(thm)],[44, 42])).
% 0.10/0.35 tff(46,plain,
% 0.10/0.35 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, f(a))) | (~element(f(a), a)) | (~element(f(a), a)))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(47,plain,
% 0.10/0.35 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, f(a))) | (~element(f(a), a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.10/0.35 tff(48,plain,
% 0.10/0.35 ($false),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[47, 41, 31, 16])).
% 0.10/0.35 tff(49,plain,(element(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.10/0.35 tff(50,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, a))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, a)))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(51,plain,
% 0.10/0.35 (((~element(a, a)) | (~element(a, a)) | (~element(a, a))) <=> (~element(a, a))),
% 0.10/0.35 inference(rewrite,[status(thm)],[])).
% 0.10/0.35 tff(52,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, a)) | (~element(a, a)) | (~element(a, a)))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, a)))),
% 0.10/0.35 inference(monotonicity,[status(thm)],[51])).
% 0.10/0.35 tff(53,plain,
% 0.10/0.35 (((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, a)) | (~element(a, a)) | (~element(a, a)))) <=> ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, a)))),
% 0.10/0.35 inference(transitivity,[status(thm)],[52, 50])).
% 0.10/0.35 tff(54,plain,
% 0.10/0.35 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | ((~element(a, a)) | (~element(a, a)) | (~element(a, a)))),
% 0.10/0.35 inference(quant_inst,[status(thm)],[])).
% 0.10/0.35 tff(55,plain,
% 0.10/0.35 ((~![Y: $i, X: $i] : ((~element(Y, X)) | (~element(X, Y)) | (~element(X, a)))) | (~element(a, a))),
% 0.10/0.35 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.10/0.35 tff(56,plain,
% 0.10/0.35 ($false),
% 0.10/0.35 inference(unit_resolution,[status(thm)],[55, 41, 49])).
% 0.10/0.35 % SZS output end Proof
%------------------------------------------------------------------------------