TSTP Solution File: ARI640_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI640_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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 17:02:25 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ARI640_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 : n017.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 00:39:50 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.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  tff(y_type, type, (
% 0.20/0.39     y: $real)).
% 0.20/0.39  tff(x_type, type, (
% 0.20/0.39     x: $real)).
% 0.20/0.39  tff(1,plain,
% 0.20/0.39      ($greater(y, 0) <=> (~$lesseq(y, 0))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(2,axiom,($greater(y, 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_01')).
% 0.20/0.39  tff(3,plain,
% 0.20/0.39      (~$lesseq(y, 0)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.39  tff(4,plain,
% 0.20/0.39      ((~$lesseq($product(x, y), $sum(x, y))) <=> (~$greatereq($sum(x, $sum(y, $product(-1, $product(x, y)))), 0))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(5,plain,
% 0.20/0.39      ($greater($product(x, y), $sum(x, y)) <=> (~$lesseq($product(x, y), $sum(x, y)))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(6,axiom,($greater($product(x, y), $sum(x, y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_03')).
% 0.20/0.39  tff(7,plain,
% 0.20/0.39      (~$lesseq($product(x, y), $sum(x, y))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39  tff(8,plain,
% 0.20/0.39      (~$greatereq($sum(x, $sum(y, $product(-1, $product(x, y)))), 0)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.39  tff(9,plain,
% 0.20/0.39      ($greater(x, 0) <=> (~$lesseq(x, 0))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(10,axiom,($greater(x, 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis')).
% 0.20/0.39  tff(11,plain,
% 0.20/0.39      (~$lesseq(x, 0)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.39  tff(12,assumption,(~$lesseq(x, 1/2)), introduced(assumption)).
% 0.20/0.39  tff(13,assumption,(~$lesseq(y, 1/2)), introduced(assumption)).
% 0.20/0.39  tff(14,assumption,(~$lesseq(x, 2/3)), introduced(assumption)).
% 0.20/0.39  tff(15,assumption,(~$lesseq(y, 2/3)), introduced(assumption)).
% 0.20/0.39  tff(16,assumption,(~$greatereq($product(x, y), 13/18)), introduced(assumption)).
% 0.20/0.39  tff(17,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(theory_lemma,[status(thm)],[8, 15, 16, 14])).
% 0.20/0.39  tff(18,plain,($greatereq($product(x, y), 13/18) | $lesseq(y, 2/3) | $lesseq(x, 2/3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39  tff(19,plain,
% 0.20/0.39      ($greatereq($product(x, y), 13/18)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[18, 15, 14])).
% 0.20/0.39  tff(20,assumption,(~$lesseq(x, 13/18)), introduced(assumption)).
% 0.20/0.39  tff(21,assumption,(~$lesseq(y, 13/18)), introduced(assumption)).
% 0.20/0.39  tff(22,plain,
% 0.20/0.39      ((~$lesseq(1, y)) <=> (~$greatereq(y, 1))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(23,plain,
% 0.20/0.39      ($less(y, 1) <=> (~$lesseq(1, y))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(24,axiom,($less(y, 1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_02')).
% 0.20/0.39  tff(25,plain,
% 0.20/0.39      (~$lesseq(1, y)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39  tff(26,plain,
% 0.20/0.39      (~$greatereq(y, 1)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.39  tff(27,plain,
% 0.20/0.39      ($lesseq(x, 13/18) | $greatereq(y, 1) | $lesseq(y, 13/18) | $greatereq($sum(x, $sum(y, $product(-1, $product(x, y)))), 0)),
% 0.20/0.39      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39  tff(28,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[27, 26, 8, 20, 21])).
% 0.20/0.39  tff(29,plain,($lesseq(y, 13/18) | $lesseq(x, 13/18)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39  tff(30,plain,
% 0.20/0.39      ($lesseq(y, 13/18)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[29, 20])).
% 0.20/0.39  tff(31,plain,
% 0.20/0.39      ($lesseq(x, 0) | (~$lesseq(y, 13/18)) | $greatereq($sum($product(13/18, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.39      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39  tff(32,plain,
% 0.20/0.39      ((~$lesseq(y, 13/18)) | $greatereq($sum($product(13/18, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[31, 11])).
% 0.20/0.39  tff(33,plain,
% 0.20/0.39      ($greatereq($sum($product(13/18, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[32, 30])).
% 0.20/0.39  tff(34,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(theory_lemma,[status(thm)],[20, 33, 8, 15])).
% 0.20/0.39  tff(35,plain,($lesseq(x, 13/18) | $lesseq(y, 2/3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39  tff(36,plain,
% 0.20/0.39      ($lesseq(x, 13/18)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[35, 15])).
% 0.20/0.39  tff(37,plain,
% 0.20/0.39      ((~$lesseq(x, 13/18)) | (~$greatereq($product(x, y), 13/18)) | $greatereq(y, 1) | $lesseq(y, 2/3)),
% 0.20/0.39      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39  tff(38,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[37, 26, 15, 36, 19])).
% 0.20/0.40  tff(39,plain,($lesseq(y, 2/3) | $lesseq(x, 2/3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40  tff(40,plain,
% 0.20/0.40      ($lesseq(y, 2/3)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[39, 14])).
% 0.20/0.40  tff(41,plain,
% 0.20/0.40      ($lesseq(x, 0) | (~$lesseq(y, 2/3)) | $greatereq($sum($product(2/3, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40  tff(42,plain,
% 0.20/0.40      ((~$lesseq(y, 2/3)) | $greatereq($sum($product(2/3, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[41, 11])).
% 0.20/0.40  tff(43,plain,
% 0.20/0.40      ($greatereq($sum($product(2/3, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[42, 40])).
% 0.20/0.40  tff(44,plain,
% 0.20/0.40      ($false),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[43, 14, 8, 13])).
% 0.20/0.40  tff(45,plain,($lesseq(x, 2/3) | $lesseq(y, 1/2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40  tff(46,plain,
% 0.20/0.40      ($lesseq(x, 2/3)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[45, 13])).
% 0.20/0.40  tff(47,plain,
% 0.20/0.40      ($lesseq(y, 0) | (~$lesseq(x, 2/3)) | $greatereq($sum($product(2/3, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40  tff(48,plain,
% 0.20/0.40      ((~$lesseq(x, 2/3)) | $greatereq($sum($product(2/3, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[47, 3])).
% 0.20/0.40  tff(49,plain,
% 0.20/0.40      ($greatereq($sum($product(2/3, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[48, 46])).
% 0.20/0.40  tff(50,plain,
% 0.20/0.40      ($false),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[49, 13, 8, 12])).
% 0.20/0.40  tff(51,plain,($lesseq(y, 1/2) | $lesseq(x, 1/2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40  tff(52,plain,
% 0.20/0.40      ($lesseq(y, 1/2)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[51, 12])).
% 0.20/0.40  tff(53,plain,
% 0.20/0.40      ($lesseq(x, 0) | (~$lesseq(y, 1/2)) | $greatereq($sum($product(1/2, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40  tff(54,plain,
% 0.20/0.40      ((~$lesseq(y, 1/2)) | $greatereq($sum($product(1/2, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[53, 11])).
% 0.20/0.40  tff(55,plain,
% 0.20/0.40      ($greatereq($sum($product(1/2, x), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[54, 52])).
% 0.20/0.40  tff(56,plain,
% 0.20/0.40      ($false),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[3, 55, 8, 12])).
% 0.20/0.40  tff(57,plain,($lesseq(x, 1/2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40  tff(58,plain,
% 0.20/0.40      ($lesseq(y, 0) | (~$lesseq(x, 1/2)) | $greatereq($sum($product(1/2, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40  tff(59,plain,
% 0.20/0.40      ((~$lesseq(x, 1/2)) | $greatereq($sum($product(1/2, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[58, 3])).
% 0.20/0.40  tff(60,plain,
% 0.20/0.40      ($greatereq($sum($product(1/2, y), $product(-1, $product(x, y))), 0)),
% 0.20/0.40      inference(unit_resolution,[status(thm)],[59, 57])).
% 0.20/0.40  tff(61,plain,
% 0.20/0.40      ($false),
% 0.20/0.40      inference(theory_lemma,[status(thm)],[60, 11, 8, 3])).
% 0.20/0.40  % SZS output end Proof
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