TSTP Solution File: ARI701_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI701_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : ARI701_1 : TPTP v8.1.0. Released v6.3.0.
% 0.09/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.16/0.37 % Computer : n004.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue Aug 30 01:49:34 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.16/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.37 Usage: tptp [options] [-file:]file
% 0.16/0.37 -h, -? prints this message.
% 0.16/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.37 -m, -model generate model.
% 0.16/0.37 -p, -proof generate proof.
% 0.16/0.37 -c, -core generate unsat core of named formulas.
% 0.16/0.37 -st, -statistics display statistics.
% 0.16/0.37 -t:timeout set timeout (in second).
% 0.16/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.37 -<param>:<value> configuration parameter and value.
% 0.16/0.37 -o:<output-file> file to place output in.
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(y_type, type, (
% 0.23/0.42 y: $int)).
% 0.23/0.42 tff(x_type, type, (
% 0.23/0.42 x: $int)).
% 0.23/0.42 tff(a_type, type, (
% 0.23/0.42 a: $int)).
% 0.23/0.42 tff(z_type, type, (
% 0.23/0.42 z: $int)).
% 0.23/0.42 tff(1,assumption,(~$greatereq(z, 0)), introduced(assumption)).
% 0.23/0.42 tff(2,assumption,($lesseq($product(x, y), -2)), introduced(assumption)).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (($product(a, z) = 1) <=> ($product(a, z) = 1)),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(4,axiom,($product(a, z) = 1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq3')).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 ($product(a, z) = 1),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 ((~($product(a, z) = 1)) | $lesseq($product(a, z), 1)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 ($lesseq($product(a, z), 1)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.23/0.42 tff(8,plain,
% 0.23/0.42 ($greatereq(a, -1) | $greatereq(z, 0) | (~$lesseq($product(a, z), 1))),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 ($greatereq(a, -1)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[8, 7, 1])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 ((0 = $sum($product(x, y), $product(-1, a))) <=> ($sum($product(x, y), $product(-1, a)) = 0)),
% 0.23/0.42 inference(commutativity,[status(thm)],[])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (($sum($product(x, y), $product(-1, a)) = 0) <=> (0 = $sum($product(x, y), $product(-1, a)))),
% 0.23/0.42 inference(symmetry,[status(thm)],[10])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (($product(x, y) = a) <=> ($sum($product(x, y), $product(-1, a)) = 0)),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (($product(x, y) = a) <=> ($product(x, y) = a)),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(14,axiom,($product(x, y) = a), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq1')).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 ($product(x, y) = a),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 ($sum($product(x, y), $product(-1, a)) = 0),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (0 = $sum($product(x, y), $product(-1, a))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 ((~(0 = $sum($product(x, y), $product(-1, a)))) | $greatereq($sum($product(x, y), $product(-1, a)), 0)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 ($greatereq($sum($product(x, y), $product(-1, a)), 0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[19, 9, 2])).
% 0.23/0.42 tff(21,plain,((~$lesseq($product(x, y), -2)) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 (~$lesseq($product(x, y), -2)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.23/0.42 tff(23,assumption,($greatereq(a, 0)), introduced(assumption)).
% 0.23/0.42 tff(24,assumption,(~$greatereq(z, -1)), introduced(assumption)).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 ((~($product(a, z) = 1)) | $greatereq($product(a, z), 1)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 ($greatereq($product(a, z), 1)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[25, 5])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 ((~$greatereq(a, 0)) | (~$greatereq($product(a, z), 1)) | $greatereq(z, -1)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[27, 26, 23, 24])).
% 0.23/0.42 tff(29,plain,($greatereq(z, -1) | (~$greatereq(a, 0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 ($greatereq(z, -1)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[29, 23])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 ($greatereq(z, 0) | (~$greatereq(z, -1)) | (~$greatereq(a, 0)) | (~$greatereq($product(a, z), 1))),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[31, 26, 1, 23, 30])).
% 0.23/0.42 tff(33,plain,((~$greatereq(a, 0)) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (~$greatereq(a, 0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 ((~(0 = $sum($product(x, y), $product(-1, a)))) | $lesseq($sum($product(x, y), $product(-1, a)), 0)),
% 0.23/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 ($lesseq($sum($product(x, y), $product(-1, a)), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[35, 17])).
% 0.23/0.43 tff(37,assumption,(~$greatereq(a, 0)), introduced(assumption)).
% 0.23/0.43 tff(38,assumption,(~$lesseq($product(x, y), 0)), introduced(assumption)).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[38, 37, 36])).
% 0.23/0.43 tff(40,plain,($lesseq($product(x, y), 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 ($lesseq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 ($greatereq(a, 0) | (~$lesseq($sum($product(x, y), $product(-1, a)), 0)) | (~$greatereq($product(x, y), 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(43,plain,
% 0.23/0.43 ($greatereq(a, 0) | (~$greatereq($product(x, y), 0))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[42, 36])).
% 0.23/0.43 tff(44,plain,
% 0.23/0.43 (~$greatereq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.23/0.43 tff(45,assumption,(~$lesseq(y, 1)), introduced(assumption)).
% 0.23/0.43 tff(46,assumption,(~$greatereq(x, 0)), introduced(assumption)).
% 0.23/0.43 tff(47,plain,
% 0.23/0.43 ($lesseq(x, 0) | $greatereq(x, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 ($lesseq(x, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.23/0.43 tff(49,assumption,(~$lesseq(y, 0)), introduced(assumption)).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 ($lesseq(y, 0) | $lesseq($product(x, y), 0) | (~$lesseq(x, 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[50, 49, 38, 48])).
% 0.23/0.43 tff(52,plain,($lesseq(y, 0) | $lesseq($product(x, y), 0) | $greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 ($lesseq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[52, 38, 46])).
% 0.23/0.43 tff(54,assumption,($greatereq(y, 0)), introduced(assumption)).
% 0.23/0.43 tff(55,assumption,($lesseq(y, 0)), introduced(assumption)).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 ((~$lesseq(y, 0)) | (~$greatereq(y, 0)) | $lesseq($product(x, y), 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[56, 55, 54, 38])).
% 0.23/0.43 tff(58,plain,((~$lesseq(y, 0)) | (~$greatereq(y, 0)) | $lesseq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (~$greatereq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[58, 53, 38])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 ((~$greatereq(x, 1)) | $greatereq(x, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (~$greatereq(x, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[60, 46])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 ((~$greatereq(z, 1)) | $greatereq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 (~$greatereq(z, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[62, 1])).
% 0.23/0.43 tff(64,assumption,(~$greatereq(y, 0)), introduced(assumption)).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 ((~$greatereq(y, 1)) | $greatereq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 (~$greatereq(y, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.23/0.43 tff(67,assumption,(~$greatereq(x, 1)), introduced(assumption)).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 ((~(z = 0)) | (~$greatereq($product(a, z), 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 (~(z = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[68, 26])).
% 0.23/0.43 tff(70,assumption,(~$greatereq($product(x, $product(y, z)), 1)), introduced(assumption)).
% 0.23/0.43 tff(71,plain,
% 0.23/0.43 ((~$greatereq(a, 0)) | (~$greatereq($product(a, z), 1)) | $greatereq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(72,plain,
% 0.23/0.43 (~$greatereq(a, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[71, 26, 1])).
% 0.23/0.43 tff(73,plain,
% 0.23/0.43 (~$greatereq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[42, 72, 36])).
% 0.23/0.43 tff(74,plain,
% 0.23/0.43 ((~($product(x, y) = 0)) | $greatereq($product(x, y), 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(75,plain,
% 0.23/0.43 (~($product(x, y) = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.23/0.43 tff(76,plain,
% 0.23/0.43 ((~(y = 0)) | ($product(x, y) = 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 (~(y = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 ((~$greatereq(x, 0)) | $greatereq($product(x, y), 0) | $lesseq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (~$greatereq(x, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[78, 49, 73])).
% 0.23/0.43 tff(80,plain,
% 0.23/0.43 ($greatereq($product(x, $product(y, z)), 1) | $lesseq(y, 0) | $greatereq(x, 0) | $greatereq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[80, 70, 1, 49, 79])).
% 0.23/0.43 tff(82,plain,($lesseq(y, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 ($lesseq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[82, 1, 70])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 ((y = 0) | (~$lesseq(y, 0)) | (~$greatereq(y, 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(85,plain,
% 0.23/0.43 (~$greatereq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[84, 83, 77])).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 ($lesseq(x, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0) | $greatereq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(87,plain,
% 0.23/0.43 ($lesseq(x, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[86, 70, 1, 85])).
% 0.23/0.43 tff(88,plain,
% 0.23/0.43 ($greatereq($product(x, y), 0) | (~$lesseq(x, 0)) | $greatereq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[88, 85, 73, 87])).
% 0.23/0.43 tff(90,plain,($greatereq(z, 0) | $greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 ($greatereq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[90, 70])).
% 0.23/0.43 tff(92,plain,
% 0.23/0.43 ((z = 0) | (~$lesseq(z, 0)) | (~$greatereq(z, 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(93,plain,
% 0.23/0.43 (~$lesseq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[92, 91, 69])).
% 0.23/0.43 tff(94,assumption,($lesseq(a, 0)), introduced(assumption)).
% 0.23/0.43 tff(95,assumption,(~$lesseq(z, 0)), introduced(assumption)).
% 0.23/0.43 tff(96,plain,
% 0.23/0.43 ((~$lesseq(a, 0)) | $lesseq(z, 0) | (~$greatereq($product(a, z), 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(97,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[96, 26, 95, 94])).
% 0.23/0.43 tff(98,plain,((~$lesseq(a, 0)) | $lesseq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(99,plain,
% 0.23/0.43 (~$lesseq(a, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[98, 93])).
% 0.23/0.43 tff(100,plain,
% 0.23/0.43 ($lesseq(a, 0) | (~$greatereq($sum($product(x, y), $product(-1, a)), 0)) | (~$lesseq($product(x, y), 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(101,plain,
% 0.23/0.43 (~$lesseq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[100, 99, 19])).
% 0.23/0.43 tff(102,plain,
% 0.23/0.43 ($greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0) | $lesseq(z, 0) | $greatereq(x, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(103,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[102, 70, 93, 64, 46])).
% 0.23/0.43 tff(104,plain,($greatereq(x, 0) | $greatereq($product(x, $product(y, z)), 1) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(105,plain,
% 0.23/0.43 ($greatereq(x, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[104, 64, 70])).
% 0.23/0.43 tff(106,plain,
% 0.23/0.43 ($lesseq($product(x, y), 0) | (~$greatereq(x, 0)) | $greatereq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(107,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[106, 64, 101, 105])).
% 0.23/0.43 tff(108,plain,($greatereq(y, 0) | $greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(109,plain,
% 0.23/0.43 ($greatereq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[108, 70])).
% 0.23/0.43 tff(110,plain,
% 0.23/0.43 (~$lesseq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[58, 109, 101])).
% 0.23/0.43 tff(111,plain,
% 0.23/0.43 ((~$lesseq(x, 0)) | $lesseq(y, 0) | $lesseq($product(x, y), 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(112,plain,
% 0.23/0.43 (~$lesseq(x, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[111, 110, 101])).
% 0.23/0.43 tff(113,plain,
% 0.23/0.43 ($lesseq(y, 0) | $greatereq($product(x, $product(y, z)), 1) | $lesseq(z, 0) | $lesseq(x, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(114,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[113, 70, 93, 110, 112])).
% 0.23/0.43 tff(115,plain,($greatereq($product(x, $product(y, z)), 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(116,plain,
% 0.23/0.43 ((1 = $product(x, $product(y, z))) <=> ($product(x, $product(y, z)) = 1)),
% 0.23/0.43 inference(commutativity,[status(thm)],[])).
% 0.23/0.43 tff(117,plain,
% 0.23/0.43 (($product(x, $product(y, z)) = 1) <=> (1 = $product(x, $product(y, z)))),
% 0.23/0.43 inference(symmetry,[status(thm)],[116])).
% 0.23/0.43 tff(118,plain,
% 0.23/0.43 ((~($product(x, $product(y, z)) = 1)) <=> (~(1 = $product(x, $product(y, z))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.23/0.43 tff(119,plain,
% 0.23/0.43 ((~($product(x, $product(y, z)) = 1)) <=> (~($product(x, $product(y, z)) = 1))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(120,plain,
% 0.23/0.43 ((~($product($product(z, y), x) = 1)) <=> (~($product(x, $product(y, z)) = 1))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(121,axiom,(~($product($product(z, y), x) = 1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.23/0.43 tff(122,plain,
% 0.23/0.43 (~($product(x, $product(y, z)) = 1)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.23/0.43 tff(123,plain,
% 0.23/0.43 (~($product(x, $product(y, z)) = 1)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.23/0.43 tff(124,plain,
% 0.23/0.43 (~(1 = $product(x, $product(y, z)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[123, 118])).
% 0.23/0.43 tff(125,plain,
% 0.23/0.43 ((1 = $product(x, $product(y, z))) | (~$lesseq($product(x, $product(y, z)), 1)) | (~$greatereq($product(x, $product(y, z)), 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(126,plain,
% 0.23/0.43 ((~$lesseq($product(x, $product(y, z)), 1)) | (~$greatereq($product(x, $product(y, z)), 1))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.23/0.43 tff(127,plain,
% 0.23/0.43 (~$lesseq($product(x, $product(y, z)), 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[126, 115])).
% 0.23/0.43 tff(128,plain,
% 0.23/0.43 ($lesseq($product(x, $product(y, z)), 1) | $greatereq(z, 1) | $greatereq(x, 1) | $greatereq(y, 1)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(129,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[128, 127, 67, 66, 63])).
% 0.23/0.43 tff(130,plain,($greatereq(x, 1) | $greatereq(z, 0) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(131,plain,
% 0.23/0.43 ($greatereq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[130, 61, 59])).
% 0.23/0.43 tff(132,plain,
% 0.23/0.43 ($greatereq($product(x, y), 0) | $lesseq($product(x, y), 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(133,plain,
% 0.23/0.43 ($greatereq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[132, 38])).
% 0.23/0.43 tff(134,assumption,($greatereq($product(x, y), 0)), introduced(assumption)).
% 0.23/0.43 tff(135,plain,
% 0.23/0.43 ((~(z = 0)) | $lesseq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(136,plain,
% 0.23/0.43 (~(z = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[135, 95])).
% 0.23/0.43 tff(137,assumption,(~(z = 0)), introduced(assumption)).
% 0.23/0.43 tff(138,assumption,(~$greatereq($sum($product(a, z), $product(-1, a)), 0)), introduced(assumption)).
% 0.23/0.43 tff(139,plain,
% 0.23/0.43 ($greatereq($sum($product(a, z), $product(-1, a)), 0) | (z = 0) | (~$greatereq($product(a, z), 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(140,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[139, 26, 138, 137])).
% 0.23/0.43 tff(141,plain,((z = 0) | $greatereq($sum($product(a, z), $product(-1, a)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(142,plain,
% 0.23/0.43 ($greatereq($sum($product(a, z), $product(-1, a)), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[141, 136])).
% 0.23/0.43 tff(143,plain,
% 0.23/0.43 ((~(x = 0)) | $greatereq(x, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(144,plain,
% 0.23/0.43 (~(x = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[143, 46])).
% 0.23/0.43 tff(145,plain,
% 0.23/0.43 ((x = 0) | $greatereq($sum($product(x, y), y), 0) | (~$greatereq($product(x, y), 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(146,plain,
% 0.23/0.43 ($greatereq($sum($product(x, y), y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[145, 134, 144])).
% 0.23/0.43 tff(147,assumption,(~$greatereq(y, -1)), introduced(assumption)).
% 0.23/0.43 tff(148,plain,
% 0.23/0.43 ($lesseq(y, -2) | $greatereq(y, -1)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(149,plain,
% 0.23/0.43 ($lesseq(y, -2)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.23/0.43 tff(150,assumption,($greatereq($sum($product(a, z), $product(-1, a)), 0)), introduced(assumption)).
% 0.23/0.43 tff(151,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[150, 36, 7, 149, 146])).
% 0.23/0.43 tff(152,plain,($greatereq(y, -1) | (~$greatereq($sum($product(a, z), $product(-1, a)), 0)) | (~$greatereq($product(x, y), 0)) | $greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(153,plain,
% 0.23/0.43 ($greatereq(y, -1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[152, 142, 134, 46])).
% 0.23/0.43 tff(154,plain,
% 0.23/0.43 ((~$lesseq(y, -2)) | (~$greatereq(y, -1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(155,plain,
% 0.23/0.43 (~$lesseq(y, -2)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.23/0.43 tff(156,plain,
% 0.23/0.43 ((~(y = 0)) | $greatereq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(157,plain,
% 0.23/0.43 (~(y = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[156, 64])).
% 0.23/0.43 tff(158,plain,
% 0.23/0.43 ((~$greatereq($product(x, y), 0)) | $greatereq($sum($product(x, y), x), 0) | (y = 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(159,plain,
% 0.23/0.43 ($greatereq($sum($product(x, y), x), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[158, 134, 157])).
% 0.23/0.43 tff(160,assumption,(~$greatereq(x, -1)), introduced(assumption)).
% 0.23/0.43 tff(161,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[160, 36, 7, 150, 159])).
% 0.23/0.43 tff(162,plain,((~$greatereq($sum($product(a, z), $product(-1, a)), 0)) | $greatereq(x, -1) | (~$greatereq($product(x, y), 0)) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(163,plain,
% 0.23/0.43 ($greatereq(x, -1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[162, 142, 134, 64])).
% 0.23/0.43 tff(164,plain,
% 0.23/0.43 (~$lesseq(a, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.23/0.43 tff(165,assumption,(~$lesseq(z, 1)), introduced(assumption)).
% 0.23/0.43 tff(166,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.23/0.43 tff(167,plain,
% 0.23/0.43 ($lesseq(a, 0) | $lesseq(z, 1) | (~$lesseq($product(a, z), 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(168,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[167, 7, 166, 165])).
% 0.23/0.43 tff(169,plain,($lesseq(z, 1) | $lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(170,plain,
% 0.23/0.43 ($lesseq(z, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[169, 164])).
% 0.23/0.43 tff(171,plain,
% 0.23/0.43 ($lesseq(y, -2) | (~$lesseq(z, 1)) | $lesseq($product(x, $product(y, z)), 1) | $greatereq(x, 0) | $lesseq(z, 0) | (~$greatereq(x, -1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(172,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[171, 127, 95, 46, 170, 163, 155])).
% 0.23/0.43 tff(173,plain,($lesseq(z, 0) | $greatereq(x, 0) | (~$greatereq($product(x, y), 0)) | $greatereq(y, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(174,plain,
% 0.23/0.43 ($lesseq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[173, 133, 46, 59])).
% 0.23/0.43 tff(175,plain,
% 0.23/0.43 ($lesseq($product(x, $product(y, z)), 1) | (~$lesseq(z, 0)) | (~$greatereq(z, 0))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(176,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[175, 127, 174, 131])).
% 0.23/0.43 tff(177,plain,($lesseq($product(x, y), 0) | $greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(178,plain,
% 0.23/0.43 ($lesseq($product(x, y), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[177, 46])).
% 0.23/0.43 tff(179,plain,
% 0.23/0.43 ($lesseq(a, 0) | (~$lesseq($product(x, y), 0))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[100, 19])).
% 0.23/0.43 tff(180,plain,
% 0.23/0.43 ($lesseq(a, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.23/0.43 tff(181,plain,
% 0.23/0.43 ($lesseq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[98, 180])).
% 0.23/0.43 tff(182,assumption,($greatereq(z, 0)), introduced(assumption)).
% 0.23/0.43 tff(183,assumption,($lesseq(z, 0)), introduced(assumption)).
% 0.23/0.43 tff(184,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[175, 127, 183, 182])).
% 0.23/0.43 tff(185,plain,((~$greatereq(z, 0)) | (~$lesseq(z, 0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(186,plain,
% 0.23/0.43 (~$greatereq(z, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[185, 181])).
% 0.23/0.43 tff(187,plain,
% 0.23/0.43 (~$lesseq($product(x, y), -2)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[21, 186])).
% 0.23/0.43 tff(188,plain,
% 0.23/0.43 ((~$lesseq(y, 0)) | $lesseq($product(x, $product(y, z)), 1) | $greatereq(x, 0) | $greatereq(z, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(189,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[188, 127, 186, 55, 46])).
% 0.23/0.43 tff(190,plain,((~$lesseq(y, 0)) | $greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(191,plain,
% 0.23/0.43 (~$lesseq(y, 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[190, 46])).
% 0.23/0.43 tff(192,assumption,($lesseq($product(x, y), 0)), introduced(assumption)).
% 0.23/0.43 tff(193,assumption,($lesseq(y, 1)), introduced(assumption)).
% 0.23/0.43 tff(194,plain,
% 0.23/0.43 ((0 = $sum($product(x, y), $product(-1, x))) <=> ($sum($product(x, y), $product(-1, x)) = 0)),
% 0.23/0.43 inference(commutativity,[status(thm)],[])).
% 0.23/0.43 tff(195,plain,
% 0.23/0.43 (($sum($product(x, y), $product(-1, x)) = 0) <=> (0 = $sum($product(x, y), $product(-1, x)))),
% 0.23/0.43 inference(symmetry,[status(thm)],[194])).
% 0.23/0.43 tff(196,assumption,($sum($product(x, y), $product(-1, x)) = 0), introduced(assumption)).
% 0.23/0.43 tff(197,plain,
% 0.23/0.43 (0 = $sum($product(x, y), $product(-1, x))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.23/0.43 tff(198,plain,
% 0.23/0.43 ((~(0 = $sum($product(x, y), $product(-1, x)))) | $greatereq($sum($product(x, y), $product(-1, x)), 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(199,plain,
% 0.23/0.43 ($greatereq($sum($product(x, y), $product(-1, x)), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.23/0.43 tff(200,plain,
% 0.23/0.43 ((~$lesseq($product(x, y), 0)) | $lesseq($sum($product(x, y), $product(-1, x)), 0) | $lesseq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(201,plain,
% 0.23/0.43 ($lesseq($sum($product(x, y), $product(-1, x)), 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[200, 49, 192])).
% 0.23/0.43 tff(202,plain,
% 0.23/0.43 ($greatereq(y, 1) | $lesseq(y, 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(203,plain,
% 0.23/0.43 ($greatereq(y, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[202, 49])).
% 0.23/0.43 tff(204,plain,
% 0.23/0.43 ((~$greatereq($sum($product(x, y), $product(-1, x)), 0)) | $lesseq($product(x, $product(y, z)), 1) | (~$lesseq(y, 1)) | (~$lesseq($sum($product(x, y), $product(-1, a)), 0)) | (~$greatereq($sum($product(x, y), $product(-1, a)), 0)) | (~$lesseq($sum($product(x, y), $product(-1, x)), 0)) | (~$lesseq($product(a, z), 1)) | (~$greatereq($product(a, z), 1)) | (~$greatereq(y, 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(205,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[204, 36, 19, 7, 26, 127, 193, 203, 201, 199])).
% 0.23/0.43 tff(206,plain,((~($sum($product(x, y), $product(-1, x)) = 0)) | (~$lesseq(y, 1)) | $lesseq(y, 0) | (~$lesseq($product(x, y), 0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(207,plain,
% 0.23/0.43 (~($sum($product(x, y), $product(-1, x)) = 0)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[206, 193, 49, 192])).
% 0.23/0.43 tff(208,plain,
% 0.23/0.43 ((y = 1) | (~$lesseq(y, 1)) | (~$greatereq(y, 1))),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(209,plain,
% 0.23/0.43 (y = 1),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[208, 193, 203])).
% 0.23/0.43 tff(210,assumption,(y = 1), introduced(assumption)).
% 0.23/0.43 tff(211,assumption,(~($sum($product(x, y), $product(-1, x)) = 0)), introduced(assumption)).
% 0.23/0.43 tff(212,plain,
% 0.23/0.43 ((~(y = 1)) | ($sum($product(x, y), $product(-1, x)) = 0)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(213,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[212, 211, 210])).
% 0.23/0.43 tff(214,plain,((~(y = 1)) | ($sum($product(x, y), $product(-1, x)) = 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(215,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[214, 209, 207])).
% 0.23/0.43 tff(216,plain,((~$lesseq(y, 1)) | $lesseq(y, 0) | (~$lesseq($product(x, y), 0))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(217,plain,
% 0.23/0.43 (~$lesseq(y, 1)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[216, 191, 178])).
% 0.23/0.43 tff(218,plain,
% 0.23/0.43 ($greatereq(x, 0) | $lesseq($product(x, y), -2) | $lesseq(y, 1)),
% 0.23/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.43 tff(219,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[218, 46, 217, 187])).
% 0.23/0.44 tff(220,plain,($greatereq(x, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(221,assumption,(~$greatereq($product(x, y), 0)), introduced(assumption)).
% 0.23/0.44 tff(222,plain,
% 0.23/0.44 ($greatereq($product(x, y), 0) | (~$greatereq(x, 0)) | $lesseq(y, 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(223,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[222, 221, 220, 45])).
% 0.23/0.44 tff(224,plain,($lesseq(y, 1) | $greatereq($product(x, y), 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(225,plain,
% 0.23/0.44 ($lesseq(y, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[224, 44])).
% 0.23/0.44 tff(226,plain,
% 0.23/0.44 ($lesseq(y, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[216, 225, 41])).
% 0.23/0.44 tff(227,plain,
% 0.23/0.44 ((~$greatereq(y, 1)) | (~$lesseq(y, 0))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(228,plain,
% 0.23/0.44 (~$greatereq(y, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.23/0.44 tff(229,assumption,(~$greatereq(y, 1)), introduced(assumption)).
% 0.23/0.44 tff(230,assumption,($lesseq(x, 0)), introduced(assumption)).
% 0.23/0.44 tff(231,plain,
% 0.23/0.44 ((~$lesseq(x, 0)) | (~$greatereq(y, 0)) | $greatereq($product(x, y), 0) | $greatereq(y, 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(232,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[231, 54, 221, 230, 229])).
% 0.23/0.44 tff(233,plain,((~$lesseq(x, 0)) | (~$greatereq(y, 0)) | $greatereq($product(x, y), 0) | $greatereq(y, 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(234,plain,
% 0.23/0.44 (~$lesseq(x, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[233, 54, 44, 228])).
% 0.23/0.44 tff(235,plain,
% 0.23/0.44 ($lesseq($product(x, $product(y, z)), 1) | $lesseq(x, 0) | $greatereq(z, 0) | (~$greatereq(y, 0))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(236,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[235, 127, 1, 54, 234])).
% 0.23/0.44 tff(237,plain,((~$greatereq(y, 0)) | $greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(238,plain,
% 0.23/0.44 (~$greatereq(y, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[237, 1])).
% 0.23/0.44 tff(239,plain,
% 0.23/0.44 ($greatereq(x, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[130, 238, 1])).
% 0.23/0.44 tff(240,plain,
% 0.23/0.44 ((~$greatereq(x, 1)) | (~$lesseq(x, 0))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(241,plain,
% 0.23/0.44 (~$lesseq(x, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.23/0.44 tff(242,assumption,(~$lesseq($product(x, y), -2)), introduced(assumption)).
% 0.23/0.44 tff(243,assumption,(~$lesseq(x, 1)), introduced(assumption)).
% 0.23/0.44 tff(244,plain,
% 0.23/0.44 ($lesseq($product(x, y), -2) | $lesseq(x, 1) | $greatereq(y, 0)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(245,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[244, 64, 243, 242])).
% 0.23/0.44 tff(246,plain,($lesseq(x, 1) | $greatereq(y, 0) | $lesseq($product(x, y), -2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(247,plain,
% 0.23/0.44 ($lesseq(x, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[246, 238, 22])).
% 0.23/0.44 tff(248,plain,
% 0.23/0.44 ((x = 1) | (~$lesseq(x, 1)) | (~$greatereq(x, 1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(249,plain,
% 0.23/0.44 ((x = 1) | (~$lesseq(x, 1))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[248, 239])).
% 0.23/0.44 tff(250,plain,
% 0.23/0.44 (x = 1),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[249, 247])).
% 0.23/0.44 tff(251,assumption,($greatereq(y, -1)), introduced(assumption)).
% 0.23/0.44 tff(252,plain,
% 0.23/0.44 ($lesseq(y, -1) | $greatereq(y, 0)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(253,plain,
% 0.23/0.44 ($lesseq(y, -1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[252, 238])).
% 0.23/0.44 tff(254,plain,
% 0.23/0.44 ((y = -1) | (~$lesseq(y, -1)) | (~$greatereq(y, -1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(255,plain,
% 0.23/0.44 (y = -1),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[254, 253, 251])).
% 0.23/0.44 tff(256,assumption,(x = 1), introduced(assumption)).
% 0.23/0.44 tff(257,plain,
% 0.23/0.44 ($greatereq(a, 0) | $greatereq(z, -1) | (~$lesseq($product(a, z), 1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(258,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[257, 7, 37, 24])).
% 0.23/0.44 tff(259,plain,($greatereq(z, -1) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(260,plain,
% 0.23/0.44 ($greatereq(z, -1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[259, 34])).
% 0.23/0.44 tff(261,plain,
% 0.23/0.44 ((~(x = 1)) | (~(y = -1)) | $lesseq($product(x, $product(y, z)), 1) | $greatereq(z, 0) | (~$greatereq(z, -1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(262,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[261, 127, 1, 260, 256, 255])).
% 0.23/0.44 tff(263,plain,((~(x = 1)) | $greatereq(z, 0) | (~$greatereq(y, -1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(264,plain,
% 0.23/0.44 (~$greatereq(y, -1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[263, 250, 1])).
% 0.23/0.44 tff(265,plain,
% 0.23/0.44 ($lesseq(y, -2)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[148, 264])).
% 0.23/0.44 tff(266,assumption,($lesseq(y, -2)), introduced(assumption)).
% 0.23/0.44 tff(267,assumption,(~$lesseq(x, 0)), introduced(assumption)).
% 0.23/0.44 tff(268,plain,
% 0.23/0.44 ($lesseq(x, 0) | $lesseq($product(x, y), -2) | (~$lesseq(y, -2))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(269,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[268, 267, 242, 266])).
% 0.23/0.44 tff(270,plain,((~$lesseq(y, -2)) | $lesseq(x, 0) | $lesseq($product(x, y), -2)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(271,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[270, 265, 241, 22])).
% 0.23/0.44 tff(272,plain,($greatereq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(273,plain,
% 0.23/0.44 (~$lesseq(z, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[185, 272])).
% 0.23/0.44 tff(274,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[141, 136, 138])).
% 0.23/0.44 tff(275,plain,($greatereq($sum($product(a, z), $product(-1, a)), 0) | $lesseq(z, 0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(276,plain,
% 0.23/0.44 ($greatereq($sum($product(a, z), $product(-1, a)), 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[275, 273])).
% 0.23/0.44 tff(277,plain,
% 0.23/0.44 ((~$lesseq($sum($product(x, y), $product(-1, a)), 0)) | (~$lesseq($product(a, z), 1)) | (~$greatereq($sum($product(a, z), $product(-1, a)), 0)) | $lesseq($product(x, y), 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(278,plain,
% 0.23/0.44 ((~$greatereq($sum($product(a, z), $product(-1, a)), 0)) | $lesseq($product(x, y), 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[277, 7, 36])).
% 0.23/0.44 tff(279,plain,
% 0.23/0.44 ($lesseq($product(x, y), 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[278, 276])).
% 0.23/0.44 tff(280,plain,
% 0.23/0.44 ((~$greatereq($product(x, y), 2)) | (~$lesseq($product(x, y), 1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(281,plain,
% 0.23/0.44 (~$greatereq($product(x, y), 2)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.23/0.44 tff(282,plain,
% 0.23/0.44 ($lesseq($product(x, $product(y, z)), 1) | (~$greatereq(x, 0)) | $greatereq(x, 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(283,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[282, 127, 220, 67])).
% 0.23/0.44 tff(284,plain,($greatereq(x, 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(285,assumption,($greatereq(x, 1)), introduced(assumption)).
% 0.23/0.44 tff(286,plain,
% 0.23/0.44 ($lesseq($product(x, $product(y, z)), 1) | $lesseq(z, 0) | (~$greatereq(x, 1)) | $greatereq(y, 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(287,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[286, 127, 273, 285, 229])).
% 0.23/0.44 tff(288,plain,((~$greatereq(x, 1)) | $greatereq(y, 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(289,plain,
% 0.23/0.44 ($greatereq(y, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[288, 284])).
% 0.23/0.44 tff(290,assumption,(~$greatereq($product(x, y), 2)), introduced(assumption)).
% 0.23/0.44 tff(291,plain,
% 0.23/0.44 ($greatereq($product(x, y), 2) | (~$greatereq(x, 1)) | $lesseq(y, 1)),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(292,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[291, 284, 45, 290])).
% 0.23/0.44 tff(293,plain,($greatereq($product(x, y), 2) | $lesseq(y, 1)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(294,plain,
% 0.23/0.44 ($lesseq(y, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[293, 281])).
% 0.23/0.44 tff(295,plain,
% 0.23/0.44 (~$lesseq(a, 0)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[98, 273])).
% 0.23/0.44 tff(296,plain,
% 0.23/0.44 ($lesseq(z, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[169, 295])).
% 0.23/0.44 tff(297,assumption,($lesseq(x, 1)), introduced(assumption)).
% 0.23/0.44 tff(298,plain,
% 0.23/0.44 ((~$lesseq(z, 1)) | $lesseq($product(x, $product(y, z)), 1) | $lesseq(z, 0) | (~$lesseq(x, 1)) | (~$lesseq(y, 1)) | (~$greatereq(y, 1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(299,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[298, 127, 273, 297, 193, 289, 296])).
% 0.23/0.44 tff(300,plain,((~$lesseq(y, 1)) | (~$lesseq(x, 1))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(301,plain,
% 0.23/0.44 (~$lesseq(x, 1)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[300, 294])).
% 0.23/0.44 tff(302,plain,
% 0.23/0.44 ($greatereq($product(x, y), 2) | $lesseq(x, 1) | (~$greatereq(y, 1))),
% 0.23/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.23/0.44 tff(303,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[302, 301, 289, 281])).
% 0.23/0.44 % SZS output end Proof
%------------------------------------------------------------------------------