TSTP Solution File: ARI699_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI699_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 6 17:02:39 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI699_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.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 : Tue Aug 30 02:07:50 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(z_type, type, (
% 0.21/0.40 z: $int)).
% 0.21/0.40 tff(x_type, type, (
% 0.21/0.40 x: $int)).
% 0.21/0.40 tff(y_type, type, (
% 0.21/0.40 y: $int)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z)))) <=> ($sum($product(-1, $product(z, z)), $product(x, $product(z, z))) = 0)),
% 0.21/0.40 inference(commutativity,[status(thm)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (($sum($product(-1, $product(z, z)), $product(x, $product(z, z))) = 0) <=> (0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z))))),
% 0.21/0.40 inference(symmetry,[status(thm)],[1])).
% 0.21/0.40 tff(3,assumption,(~$lesseq(x, 1)), introduced(assumption)).
% 0.21/0.40 tff(4,assumption,(~$lesseq($sum($product(-1, y), $product(x, y)), 0)), introduced(assumption)).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 ((0 = $sum(y, $product(-2, $product(z, z)))) <=> ($sum(y, $product(-2, $product(z, z))) = 0)),
% 0.21/0.40 inference(commutativity,[status(thm)],[])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (($sum(y, $product(-2, $product(z, z))) = 0) <=> (0 = $sum(y, $product(-2, $product(z, z))))),
% 0.21/0.40 inference(symmetry,[status(thm)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (($product(2, $product(z, z)) = y) <=> ($sum(y, $product(-2, $product(z, z))) = 0)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (($product(2, $product(z, z)) = y) <=> ($product(2, $product(z, z)) = y)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (($product($product(2, z), z) = y) <=> ($product(2, $product(z, z)) = y)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(10,axiom,($product($product(2, z), z) = y), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq')).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 ($product(2, $product(z, z)) = y),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ($product(2, $product(z, z)) = y),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 ($sum(y, $product(-2, $product(z, z))) = 0),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (0 = $sum(y, $product(-2, $product(z, z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~(0 = $sum(y, $product(-2, $product(z, z))))) | $greatereq($sum(y, $product(-2, $product(z, z))), 0)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 ($greatereq($sum(y, $product(-2, $product(z, z))), 0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~(0 = $sum(y, $product(-2, $product(z, z))))) | $lesseq($sum(y, $product(-2, $product(z, z))), 0)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 ($lesseq($sum(y, $product(-2, $product(z, z))), 0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 ($lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y)))) <=> $greatereq($sum($product(x, $product(z, z)), $product(-1, $product(x, y))), 0)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 ($lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y)))) <=> $lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 ($lesseq(0, $sum($product($product(z, z), x), $product(-1, $product(y, x)))) <=> $lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(22,axiom,($lesseq(0, $sum($product($product(z, z), x), $product(-1, $product(y, x))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ineq3')).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ($lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ($lesseq(0, $sum($product(x, $product(z, z)), $product(-1, $product(x, y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 ($greatereq($sum($product(x, $product(z, z)), $product(-1, $product(x, y))), 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 ((~$lesseq(y, 0)) <=> (~$lesseq(y, 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ($greater(y, 0) <=> (~$lesseq(y, 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(28,axiom,($greater(y, 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ineq2')).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (~$lesseq(y, 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (~$lesseq(y, 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 ((~$greatereq($sum(y, $product(-2, $product(z, z))), 0)) | $lesseq(y, 0) | (~$greatereq($sum($product(x, $product(z, z)), $product(-1, $product(x, y))), 0)) | $lesseq($sum($product(-1, y), $product(x, y)), 0) | (~$lesseq($sum(y, $product(-2, $product(z, z))), 0))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[31, 30, 25, 18, 16, 4])).
% 0.21/0.40 tff(33,plain,($lesseq($sum($product(-1, y), $product(x, y)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 ($lesseq(y, 0) | (~$lesseq($sum($product(-1, y), $product(x, y)), 0)) | $lesseq(x, 1)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[34, 30, 33, 3])).
% 0.21/0.40 tff(36,plain,($lesseq(x, 1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((~$lesseq(x, 0)) <=> (~$lesseq(x, 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ($greater(x, 0) <=> (~$lesseq(x, 0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(39,axiom,($greater(x, 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ineq1')).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (~$lesseq(x, 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (~$lesseq(x, 0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (($sum($product(-1, $product(z, z)), $product(x, $product(z, z))) = 0) | $lesseq(x, 0) | (~$lesseq(x, 1))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ($sum($product(-1, $product(z, z)), $product(x, $product(z, z))) = 0),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[42, 41, 36])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[43, 2])).
% 0.21/0.40 tff(45,assumption,(~(0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z))))), introduced(assumption)).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.40 tff(47,plain,(0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(48,assumption,($lesseq($sum($product(-1, $product(z, z)), $product(x, $product(z, z))), 0)), introduced(assumption)).
% 0.21/0.40 tff(49,assumption,(~$lesseq($sum(y, $product(-1, $product(x, y))), 0)), introduced(assumption)).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ($greatereq($product(x, y), 1) | $lesseq(x, 0) | $lesseq(y, 0)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ($greatereq($product(x, y), 1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[50, 41, 30])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 ($lesseq($sum(y, $product(-1, $product(x, y))), 0) | $lesseq(x, 0) | (~$greatereq($product(x, y), 1))),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[52, 41, 51, 49])).
% 0.21/0.40 tff(54,plain,($lesseq($sum(y, $product(-1, $product(x, y))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[16, 30, 54, 25, 48])).
% 0.21/0.40 tff(56,plain,(~$lesseq($sum($product(-1, $product(z, z)), $product(x, $product(z, z))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 ((~(0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z))))) | $lesseq($sum($product(-1, $product(z, z)), $product(x, $product(z, z))), 0)),
% 0.21/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (~(0 = $sum($product(-1, $product(z, z)), $product(x, $product(z, z))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[58, 47])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------