TSTP Solution File: ARI640_1 by Z3---4.8.9.0
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- 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
%------------------------------------------------------------------------------