TSTP Solution File: SYN009-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN009-1 : 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 : Thu Sep 29 23:53:09 EDT 2022
% Result : Unsatisfiable 0.11s 0.29s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYN009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n021.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Sep 5 00:55:31 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.27 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.27 Usage: tptp [options] [-file:]file
% 0.07/0.27 -h, -? prints this message.
% 0.07/0.27 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.27 -m, -model generate model.
% 0.07/0.27 -p, -proof generate proof.
% 0.07/0.27 -c, -core generate unsat core of named formulas.
% 0.07/0.27 -st, -statistics display statistics.
% 0.07/0.27 -t:timeout set timeout (in second).
% 0.07/0.27 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.27 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.27 -<param>:<value> configuration parameter and value.
% 0.07/0.27 -o:<output-file> file to place output in.
% 0.11/0.29 % SZS status Unsatisfiable
% 0.11/0.29 % SZS output start Proof
% 0.11/0.29 tff(r_type, type, (
% 0.11/0.29 r: ( $i * $i * $i ) > $o)).
% 0.11/0.29 tff(c_type, type, (
% 0.11/0.29 c: $i)).
% 0.11/0.29 tff(q_type, type, (
% 0.11/0.29 q: ( $i * $i * $i ) > $o)).
% 0.11/0.29 tff(p_type, type, (
% 0.11/0.29 p: ( $i * $i * $i ) > $o)).
% 0.11/0.29 tff(s_type, type, (
% 0.11/0.29 s: $i > $o)).
% 0.11/0.29 tff(1,assumption,(q(c, c, c)), introduced(assumption)).
% 0.11/0.29 tff(2,plain,
% 0.11/0.29 (^[Y: $i, X: $i] : refl((~q(X, c, Y)) <=> (~q(X, c, Y)))),
% 0.11/0.29 inference(bind,[status(th)],[])).
% 0.11/0.29 tff(3,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~q(X, c, Y)) <=> ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.11/0.29 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.29 tff(4,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~q(X, c, Y)) <=> ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.11/0.29 inference(rewrite,[status(thm)],[])).
% 0.11/0.29 tff(5,axiom,(![Y: $i, X: $i] : (~q(X, c, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.11/0.29 tff(6,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.11/0.29 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.29 tff(7,plain,(
% 0.11/0.29 ![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.11/0.29 inference(skolemize,[status(sab)],[6])).
% 0.11/0.29 tff(8,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~q(X, c, Y))),
% 0.11/0.29 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.29 tff(9,plain,
% 0.11/0.29 ((~![Y: $i, X: $i] : (~q(X, c, Y))) | (~q(c, c, c))),
% 0.11/0.29 inference(quant_inst,[status(thm)],[])).
% 0.11/0.29 tff(10,plain,
% 0.11/0.29 ($false),
% 0.11/0.29 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.29 tff(11,plain,(~q(c, c, c)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.29 tff(12,assumption,(p(c, c, c)), introduced(assumption)).
% 0.11/0.29 tff(13,plain,
% 0.11/0.29 (^[Y: $i, X: $i] : refl((~p(c, X, Y)) <=> (~p(c, X, Y)))),
% 0.11/0.29 inference(bind,[status(th)],[])).
% 0.11/0.29 tff(14,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~p(c, X, Y)) <=> ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.11/0.29 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.29 tff(15,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~p(c, X, Y)) <=> ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.11/0.29 inference(rewrite,[status(thm)],[])).
% 0.11/0.29 tff(16,axiom,(![Y: $i, X: $i] : (~p(c, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.11/0.29 tff(17,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.11/0.29 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.29 tff(18,plain,(
% 0.11/0.29 ![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.11/0.29 inference(skolemize,[status(sab)],[17])).
% 0.11/0.29 tff(19,plain,
% 0.11/0.29 (![Y: $i, X: $i] : (~p(c, X, Y))),
% 0.11/0.29 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.29 tff(20,plain,
% 0.11/0.29 ((~![Y: $i, X: $i] : (~p(c, X, Y))) | (~p(c, c, c))),
% 0.11/0.29 inference(quant_inst,[status(thm)],[])).
% 0.11/0.29 tff(21,plain,
% 0.11/0.29 ($false),
% 0.11/0.29 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.11/0.29 tff(22,plain,(~p(c, c, c)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.29 tff(23,plain,
% 0.11/0.29 (^[Z: $i, Y: $i, X: $i] : refl((r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))),
% 0.11/0.29 inference(bind,[status(th)],[])).
% 0.11/0.29 tff(24,plain,
% 0.11/0.29 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.29 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.29 tff(25,plain,
% 0.11/0.29 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.29 inference(rewrite,[status(thm)],[])).
% 0.11/0.29 tff(26,plain,
% 0.11/0.29 (^[Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~s(X)) | (~s(Y))) | (~s(Z))) <=> ((~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)))), rewrite((((~s(Z)) | (~s(Y)) | (~s(X))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) <=> (p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> ((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)))), rewrite(((p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | q(X, Y, Z)) <=> (q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) <=> (q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ((q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)))), rewrite(((q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X))) | r(X, Y, Z)) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))), (((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(27,plain,
% 0.11/0.30 (![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z)) <=> ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[26])).
% 0.11/0.30 tff(28,axiom,(![Z: $i, Y: $i, X: $i] : ((((((~s(X)) | (~s(Y))) | (~s(Z))) | p(X, Y, Z)) | q(X, Y, Z)) | r(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 0.11/0.30 tff(29,plain,
% 0.11/0.30 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.30 tff(30,plain,
% 0.11/0.30 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.11/0.30 tff(31,plain,(
% 0.11/0.30 ![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.30 inference(skolemize,[status(sab)],[30])).
% 0.11/0.30 tff(32,plain,
% 0.11/0.30 (![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.11/0.30 tff(33,plain,
% 0.11/0.30 (s(c) <=> s(c)),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(34,axiom,(s(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.11/0.30 tff(35,plain,
% 0.11/0.30 (s(c)),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.30 tff(36,plain,
% 0.11/0.30 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(37,plain,
% 0.11/0.30 ((r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c))) <=> ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(38,plain,
% 0.11/0.30 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | ((~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c)))),
% 0.11/0.30 inference(monotonicity,[status(thm)],[37])).
% 0.11/0.30 tff(39,plain,
% 0.11/0.30 (((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))) <=> ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c))),
% 0.11/0.30 inference(transitivity,[status(thm)],[38, 36])).
% 0.11/0.30 tff(40,plain,
% 0.11/0.30 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (r(c, c, c) | q(c, c, c) | p(c, c, c) | (~s(c)) | (~s(c)) | (~s(c)))),
% 0.11/0.30 inference(quant_inst,[status(thm)],[])).
% 0.11/0.30 tff(41,plain,
% 0.11/0.30 ((~![Z: $i, Y: $i, X: $i] : (r(X, Y, Z) | q(X, Y, Z) | p(X, Y, Z) | (~s(Z)) | (~s(Y)) | (~s(X)))) | (~s(c)) | r(c, c, c) | q(c, c, c) | p(c, c, c)),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.11/0.30 tff(42,plain,
% 0.11/0.30 (r(c, c, c) | q(c, c, c) | p(c, c, c)),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[41, 35, 32])).
% 0.11/0.30 tff(43,plain,
% 0.11/0.30 (r(c, c, c) | q(c, c, c)),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[42, 22])).
% 0.11/0.30 tff(44,plain,
% 0.11/0.30 (r(c, c, c)),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[43, 11])).
% 0.11/0.30 tff(45,plain,
% 0.11/0.30 (^[Y: $i, X: $i] : refl((~r(X, Y, c)) <=> (~r(X, Y, c)))),
% 0.11/0.30 inference(bind,[status(th)],[])).
% 0.11/0.30 tff(46,plain,
% 0.11/0.30 (![Y: $i, X: $i] : (~r(X, Y, c)) <=> ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.11/0.30 inference(quant_intro,[status(thm)],[45])).
% 0.11/0.30 tff(47,plain,
% 0.11/0.30 (![Y: $i, X: $i] : (~r(X, Y, c)) <=> ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.11/0.30 inference(rewrite,[status(thm)],[])).
% 0.11/0.30 tff(48,axiom,(![Y: $i, X: $i] : (~r(X, Y, c))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.11/0.30 tff(49,plain,
% 0.11/0.30 (![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.11/0.30 tff(50,plain,(
% 0.11/0.30 ![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.11/0.30 inference(skolemize,[status(sab)],[49])).
% 0.11/0.30 tff(51,plain,
% 0.11/0.30 (![Y: $i, X: $i] : (~r(X, Y, c))),
% 0.11/0.30 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.11/0.30 tff(52,plain,
% 0.11/0.30 ((~![Y: $i, X: $i] : (~r(X, Y, c))) | (~r(c, c, c))),
% 0.11/0.30 inference(quant_inst,[status(thm)],[])).
% 0.11/0.30 tff(53,plain,
% 0.11/0.30 ($false),
% 0.11/0.30 inference(unit_resolution,[status(thm)],[52, 51, 44])).
% 0.11/0.30 % SZS output end Proof
%------------------------------------------------------------------------------