TSTP Solution File: ARI702_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI702_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI702_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 01:47:52 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(a_type, type, (
% 0.13/0.40 a: $int)).
% 0.13/0.40 tff(z_type, type, (
% 0.13/0.40 z: $int)).
% 0.13/0.40 tff(y_type, type, (
% 0.13/0.40 y: $int)).
% 0.13/0.40 tff(x_type, type, (
% 0.13/0.40 x: $int)).
% 0.13/0.40 tff(1,assumption,(~$greatereq(z, 0)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((2 = $product(a, z)) <=> ($product(a, z) = 2)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (($product(a, z) = 2) <=> (2 = $product(a, z))),
% 0.13/0.40 inference(symmetry,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (($product(a, z) = 2) <=> ($product(a, z) = 2)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,axiom,($product(a, z) = 2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq3')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ($product(a, z) = 2),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (2 = $product(a, z)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~(2 = $product(a, z))) | $lesseq($product(a, z), 2)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ($lesseq($product(a, z), 2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ($greatereq(a, -2) | (~$lesseq($product(a, z), 2)) | $greatereq(z, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ($greatereq(a, -2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[10, 9, 1])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 ((0 = $sum(a, $product(-2, $product(x, y)))) <=> ($sum(a, $product(-2, $product(x, y))) = 0)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (($sum(a, $product(-2, $product(x, y))) = 0) <=> (0 = $sum(a, $product(-2, $product(x, y))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (($product(2, $product(x, y)) = a) <=> ($sum(a, $product(-2, $product(x, y))) = 0)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (($product(2, $product(x, y)) = a) <=> ($product(2, $product(x, y)) = a)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (($product($product(2, x), y) = a) <=> ($product(2, $product(x, y)) = a)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(17,axiom,($product($product(2, x), y) = a), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq1')).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ($product(2, $product(x, y)) = a),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ($product(2, $product(x, y)) = a),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ($sum(a, $product(-2, $product(x, y))) = 0),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (0 = $sum(a, $product(-2, $product(x, y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~(0 = $sum(a, $product(-2, $product(x, y))))) | $lesseq($sum(a, $product(-2, $product(x, y))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ($lesseq($sum(a, $product(-2, $product(x, y))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,assumption,(~$greatereq($product(x, y), -1)), introduced(assumption)).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[24, 23, 11])).
% 0.13/0.40 tff(26,plain,($greatereq($product(x, y), -1) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 ($greatereq($product(x, y), -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.13/0.40 tff(28,assumption,($greatereq(a, 0)), introduced(assumption)).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~(2 = $product(a, z))) | $greatereq($product(a, z), 2)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ($greatereq($product(a, z), 2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[29, 7])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~$greatereq(a, 0)) | (~$greatereq($product(a, z), 2)) | $greatereq(z, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30, 1, 28])).
% 0.13/0.40 tff(33,plain,((~$greatereq(a, 0)) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (~$greatereq(a, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ((~(0 = $sum(a, $product(-2, $product(x, y))))) | $greatereq($sum(a, $product(-2, $product(x, y))), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ($greatereq($sum(a, $product(-2, $product(x, y))), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[35, 21])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ($greatereq(a, 0) | (~$greatereq($sum(a, $product(-2, $product(x, y))), 0)) | (~$greatereq($product(x, y), 0))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ($greatereq(a, 0) | (~$greatereq($product(x, y), 0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (~$greatereq($product(x, y), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 34])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 ($lesseq($product(x, y), -1) | $greatereq($product(x, y), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 ($lesseq($product(x, y), -1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.41 tff(42,assumption,($greatereq(a, -1)), introduced(assumption)).
% 0.13/0.41 tff(43,assumption,($lesseq($product(x, y), -1)), introduced(assumption)).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[43, 23, 42])).
% 0.13/0.41 tff(45,plain,((~$greatereq(a, -1)) | (~$lesseq($product(x, y), -1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (~$greatereq(a, -1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.13/0.41 tff(47,assumption,(~$greatereq(a, -1)), introduced(assumption)).
% 0.13/0.41 tff(48,assumption,(~$greatereq(z, -1)), introduced(assumption)).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 ($greatereq(z, -1) | $greatereq(a, -1) | (~$lesseq($product(a, z), 2))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[49, 9, 48, 47])).
% 0.13/0.41 tff(51,plain,($greatereq(z, -1) | $greatereq(a, -1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 ($greatereq(z, -1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 ($lesseq(z, -1) | $greatereq(z, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ($lesseq(z, -1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[53, 1])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((z = -1) | (~$lesseq(z, -1)) | (~$greatereq(z, -1))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (z = -1),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 54, 52])).
% 0.13/0.41 tff(57,assumption,($greatereq($product(x, y), -1)), introduced(assumption)).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (($product(x, y) = -1) | (~$lesseq($product(x, y), -1)) | (~$greatereq($product(x, y), -1))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 ($product(x, y) = -1),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[58, 43, 57])).
% 0.13/0.41 tff(60,assumption,(z = -1), introduced(assumption)).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 ((~(z = 0)) | (~$greatereq($product(a, z), 2))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (~(z = 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[61, 30])).
% 0.13/0.41 tff(63,assumption,(~$greatereq($product(x, $product(y, z)), 1)), introduced(assumption)).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (~$greatereq(a, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[31, 30, 1])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 (~$greatereq($product(x, y), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 64, 36])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 ((~($product(x, y) = 0)) | $greatereq($product(x, y), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (~($product(x, y) = 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 ((~(y = 0)) | ($product(x, y) = 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (~(y = 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.13/0.41 tff(70,assumption,(~$lesseq(y, 0)), introduced(assumption)).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 ((~$greatereq(x, 0)) | $greatereq($product(x, y), 0) | $lesseq(y, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (~$greatereq(x, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[71, 70, 65])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 ($greatereq($product(x, $product(y, z)), 1) | $lesseq(y, 0) | $greatereq(x, 0) | $greatereq(z, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[73, 63, 1, 70, 72])).
% 0.13/0.41 tff(75,plain,($lesseq(y, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 ($lesseq(y, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[75, 1, 63])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 ((y = 0) | (~$lesseq(y, 0)) | (~$greatereq(y, 0))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 (~$greatereq(y, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[77, 76, 69])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 ($lesseq(x, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0) | $greatereq(z, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 ($lesseq(x, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[79, 63, 1, 78])).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 ($greatereq($product(x, y), 0) | (~$lesseq(x, 0)) | $greatereq(y, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[81, 78, 65, 80])).
% 0.13/0.41 tff(83,plain,($greatereq(z, 0) | $greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 ($greatereq(z, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[83, 63])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 ((z = 0) | (~$lesseq(z, 0)) | (~$greatereq(z, 0))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(86,plain,
% 0.13/0.41 (~$lesseq(z, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[85, 84, 62])).
% 0.13/0.41 tff(87,assumption,($lesseq(a, 0)), introduced(assumption)).
% 0.13/0.41 tff(88,assumption,(~$lesseq(z, 0)), introduced(assumption)).
% 0.13/0.41 tff(89,plain,
% 0.13/0.41 ((~$lesseq(a, 0)) | $lesseq(z, 0) | (~$greatereq($product(a, z), 2))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(90,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[89, 30, 88, 87])).
% 0.13/0.41 tff(91,plain,((~$lesseq(a, 0)) | $lesseq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(92,plain,
% 0.13/0.41 (~$lesseq(a, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[91, 86])).
% 0.13/0.41 tff(93,plain,
% 0.13/0.41 ($lesseq(a, 0) | (~$lesseq($sum(a, $product(-2, $product(x, y))), 0)) | (~$lesseq($product(x, y), 0))),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(94,plain,
% 0.13/0.41 (~$lesseq($product(x, y), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[93, 92, 23])).
% 0.13/0.41 tff(95,assumption,(~$greatereq(y, 0)), introduced(assumption)).
% 0.13/0.41 tff(96,assumption,(~$greatereq(x, 0)), introduced(assumption)).
% 0.13/0.41 tff(97,plain,
% 0.13/0.41 ($greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0) | $lesseq(z, 0) | $greatereq(x, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(98,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[97, 63, 86, 95, 96])).
% 0.13/0.41 tff(99,plain,($greatereq(x, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(100,plain,
% 0.13/0.41 ($greatereq(x, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[99, 95, 63])).
% 0.13/0.41 tff(101,plain,
% 0.13/0.41 ($lesseq($product(x, y), 0) | (~$greatereq(x, 0)) | $greatereq(y, 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(102,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[101, 95, 94, 100])).
% 0.13/0.41 tff(103,plain,($greatereq(y, 0) | $greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(104,plain,
% 0.13/0.41 ($greatereq(y, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[103, 63])).
% 0.13/0.41 tff(105,assumption,(~$lesseq($product(x, y), 0)), introduced(assumption)).
% 0.13/0.41 tff(106,assumption,($greatereq(y, 0)), introduced(assumption)).
% 0.13/0.41 tff(107,assumption,($lesseq(y, 0)), introduced(assumption)).
% 0.13/0.41 tff(108,plain,
% 0.13/0.41 ((~$lesseq(y, 0)) | (~$greatereq(y, 0)) | $lesseq($product(x, y), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(109,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[108, 107, 106, 105])).
% 0.13/0.41 tff(110,plain,((~$lesseq(y, 0)) | (~$greatereq(y, 0)) | $lesseq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(111,plain,
% 0.13/0.41 (~$lesseq(y, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[110, 104, 94])).
% 0.13/0.41 tff(112,plain,
% 0.13/0.41 ((~$lesseq(x, 0)) | $lesseq(y, 0) | $lesseq($product(x, y), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(113,plain,
% 0.13/0.41 (~$lesseq(x, 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[112, 111, 94])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ($lesseq(y, 0) | $greatereq($product(x, $product(y, z)), 1) | $lesseq(z, 0) | $lesseq(x, 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[114, 63, 86, 111, 113])).
% 0.21/0.41 tff(116,plain,($greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 ((1 = $product(x, $product(y, z))) <=> ($product(x, $product(y, z)) = 1)),
% 0.21/0.41 inference(commutativity,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 (($product(x, $product(y, z)) = 1) <=> (1 = $product(x, $product(y, z)))),
% 0.21/0.41 inference(symmetry,[status(thm)],[117])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 ((~($product(x, $product(y, z)) = 1)) <=> (~(1 = $product(x, $product(y, z))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 ((~($product(x, $product(y, z)) = 1)) <=> (~($product(x, $product(y, z)) = 1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~($product($product(x, y), z) = 1)) <=> (~($product(x, $product(y, z)) = 1))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(122,axiom,(~($product($product(x, y), z) = 1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (~($product(x, $product(y, z)) = 1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (~($product(x, $product(y, z)) = 1)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[123, 120])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 (~(1 = $product(x, $product(y, z)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[124, 119])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 ((1 = $product(x, $product(y, z))) | (~$lesseq($product(x, $product(y, z)), 1)) | (~$greatereq($product(x, $product(y, z)), 1))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 ((~$lesseq($product(x, $product(y, z)), 1)) | (~$greatereq($product(x, $product(y, z)), 1))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (~$lesseq($product(x, $product(y, z)), 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[127, 116])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 ((~(z = -1)) | (~($product(x, y) = -1)) | $lesseq($product(x, $product(y, z)), 1)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[129, 128, 60, 59])).
% 0.21/0.41 tff(131,plain,((~(z = -1)) | (~$lesseq($product(x, y), -1)) | (~$greatereq($product(x, y), -1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[131, 56, 41, 27])).
% 0.21/0.41 tff(133,plain,($greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(134,assumption,(~$greatereq(z, 1)), introduced(assumption)).
% 0.21/0.41 tff(135,assumption,($greatereq(z, 0)), introduced(assumption)).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 ($lesseq($product(x, $product(y, z)), 1) | $greatereq(z, 1) | (~$greatereq(z, 0))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[136, 128, 135, 134])).
% 0.21/0.41 tff(138,plain,($greatereq(z, 1) | (~$greatereq(z, 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 ($greatereq(z, 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[138, 133])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 ((~$greatereq(z, 1)) | (~$lesseq(z, 0))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (~$lesseq(z, 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 (~$lesseq(a, 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[91, 141])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 ($lesseq(a, 0) | (~$lesseq($product(x, y), 0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 23])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 (~$lesseq($product(x, y), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 ($greatereq($product(x, y), 1) | $lesseq($product(x, y), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 ($greatereq($product(x, y), 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.21/0.41 tff(147,assumption,(~$greatereq($sum($product(a, z), $product(-1, a)), 0)), introduced(assumption)).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 ((~(z = 0)) | $lesseq(z, 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 (~(z = 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[148, 88])).
% 0.21/0.41 tff(150,assumption,(~(z = 0)), introduced(assumption)).
% 0.21/0.41 tff(151,plain,
% 0.21/0.41 ($greatereq($sum($product(a, z), $product(-1, a)), 0) | (z = 0) | (~$greatereq($product(a, z), 2))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(152,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[151, 30, 147, 150])).
% 0.21/0.41 tff(153,plain,((z = 0) | $greatereq($sum($product(a, z), $product(-1, a)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(154,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[153, 149, 147])).
% 0.21/0.41 tff(155,plain,($greatereq($sum($product(a, z), $product(-1, a)), 0) | $lesseq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(156,plain,
% 0.21/0.41 ($greatereq($sum($product(a, z), $product(-1, a)), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[155, 141])).
% 0.21/0.41 tff(157,assumption,($greatereq($sum($product(a, z), $product(-1, a)), 0)), introduced(assumption)).
% 0.21/0.41 tff(158,assumption,(~$lesseq($product(x, y), 1)), introduced(assumption)).
% 0.21/0.41 tff(159,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[158, 36, 9, 157])).
% 0.21/0.41 tff(160,plain,((~$greatereq($sum($product(a, z), $product(-1, a)), 0)) | $lesseq($product(x, y), 1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(161,plain,
% 0.21/0.41 ($lesseq($product(x, y), 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[160, 156])).
% 0.21/0.41 tff(162,assumption,($lesseq($product(x, y), 1)), introduced(assumption)).
% 0.21/0.41 tff(163,assumption,($greatereq($product(x, y), 1)), introduced(assumption)).
% 0.21/0.41 tff(164,plain,
% 0.21/0.41 (($product(x, y) = 1) | (~$lesseq($product(x, y), 1)) | (~$greatereq($product(x, y), 1))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(165,plain,
% 0.21/0.41 ($product(x, y) = 1),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[164, 163, 162])).
% 0.21/0.41 tff(166,assumption,(z = 1), introduced(assumption)).
% 0.21/0.41 tff(167,plain,
% 0.21/0.41 ((~(z = 1)) | (~($product(x, y) = 1)) | $lesseq($product(x, $product(y, z)), 1)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(168,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[167, 128, 166, 165])).
% 0.21/0.41 tff(169,plain,((~(z = 1)) | (~$greatereq($product(x, y), 1)) | (~$lesseq($product(x, y), 1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(170,plain,
% 0.21/0.41 (~(z = 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[169, 161, 146])).
% 0.21/0.41 tff(171,plain,
% 0.21/0.41 ((z = 1) | (~$lesseq(z, 1)) | (~$greatereq(z, 1))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(172,plain,
% 0.21/0.41 (~$lesseq(z, 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[171, 170, 139])).
% 0.21/0.41 tff(173,assumption,(~$lesseq(a, 1)), introduced(assumption)).
% 0.21/0.41 tff(174,assumption,(~$lesseq(z, 1)), introduced(assumption)).
% 0.21/0.41 tff(175,plain,
% 0.21/0.41 ($lesseq(z, 1) | $lesseq(a, 1) | (~$lesseq($product(a, z), 2))),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(176,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[175, 9, 174, 173])).
% 0.21/0.41 tff(177,plain,($lesseq(z, 1) | $lesseq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(178,plain,
% 0.21/0.41 ($lesseq(a, 1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[177, 172])).
% 0.21/0.41 tff(179,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[23, 178, 36, 142])).
% 0.21/0.41 % SZS output end Proof
%------------------------------------------------------------------------------