TSTP Solution File: ARI669_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI669_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 17:02:31 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
% 0.07/0.12 % Problem : ARI669_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.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 01:25:25 EDT 2022
% 0.13/0.34 % 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(a_type, type, (
% 0.20/0.39 a: $int)).
% 0.20/0.39 tff(b_type, type, (
% 0.20/0.39 b: $int)).
% 0.20/0.39 tff(c_type, type, (
% 0.20/0.39 c: $int)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((0 = $product(a, $product(b, $product(b, c)))) <=> ($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.39 inference(commutativity,[status(thm)],[])).
% 0.20/0.39 tff(2,assumption,(~$lesseq($product(a, $product(b, $product(b, c))), 0)), introduced(assumption)).
% 0.20/0.39 tff(3,assumption,(~$greatereq(a, 0)), introduced(assumption)).
% 0.20/0.39 tff(4,assumption,(~$greatereq(b, 0)), introduced(assumption)).
% 0.20/0.39 tff(5,assumption,(~$greatereq(c, 0)), introduced(assumption)).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~(c = 0)) | $greatereq(c, 0)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~(c = 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~(a = 0)) | $greatereq(a, 0)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~(a = 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 3])).
% 0.20/0.39 tff(10,assumption,(~((c = 0) | (b = 0) | (a = 0))), introduced(assumption)).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (((c = 0) | (b = 0) | (a = 0)) | (~(b = 0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~(b = 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,assumption,(~$lesseq(b, 0)), introduced(assumption)).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (((c = 0) | (b = 0) | (a = 0)) | (~(a = 0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~(a = 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[14, 10])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (($product(a, $product(b, $product(b, c))) = 0) <=> (0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.39 inference(symmetry,[status(thm)],[1])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))) <=> ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 ((~(($product(a, $product(b, $product(b, c))) = 0) <=> ((c = 0) | (b = 0) | (a = 0)))) <=> ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((($product($product($product(a, b), b), c) = 0) <=> (((c = 0) | (b = 0)) | (a = 0))) <=> (($product(a, $product(b, $product(b, c))) = 0) <=> ((c = 0) | (b = 0) | (a = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~(($product($product($product(a, b), b), c) = 0) <=> (((c = 0) | (b = 0)) | (a = 0)))) <=> (~(($product(a, $product(b, $product(b, c))) = 0) <=> ((c = 0) | (b = 0) | (a = 0))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~(($product($product($product(a, b), b), c) = 0) <=> (((c = 0) | (b = 0)) | (a = 0)))) <=> ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.39 tff(22,axiom,(~(($product($product($product(a, b), b), c) = 0) <=> (((c = 0) | (b = 0)) | (a = 0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (($product(a, $product(b, $product(b, c))) = 0) | ((c = 0) | (b = 0) | (a = 0)) | (~((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (($product(a, $product(b, $product(b, c))) = 0) | ((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ($product(a, $product(b, $product(b, c))) = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 10])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (0 = $product(a, $product(b, $product(b, c)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 16])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~(0 = $product(a, $product(b, $product(b, c))))) | $lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((c = 0) | (b = 0) | (a = 0)) | (~(c = 0))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (~(c = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 10])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~(0 = $product(a, $product(b, $product(b, c))))) | $greatereq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.20/0.40 tff(42,assumption,(~(c = 0)), introduced(assumption)).
% 0.20/0.40 tff(43,assumption,($lesseq($product(a, $product(b, $product(b, c))), 0)), introduced(assumption)).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 ((~$lesseq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(b, 0) | $greatereq(c, 0) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[44, 43, 5, 13, 3])).
% 0.20/0.40 tff(46,plain,($greatereq(c, 0) | (~$lesseq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(b, 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ($greatereq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 3, 13, 43])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((c = 0) | (~$lesseq(c, 0)) | (~$greatereq(c, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (~$lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 47, 42])).
% 0.20/0.40 tff(50,assumption,($greatereq($product(a, $product(b, $product(b, c))), 0)), introduced(assumption)).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 ($lesseq(b, 0) | (~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(c, 0) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 50, 49, 13, 3])).
% 0.20/0.40 tff(53,plain,($greatereq(a, 0) | (~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(b, 0) | (c = 0) | (~$lesseq($product(a, $product(b, $product(b, c))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ($greatereq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 41, 13, 39, 37])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((a = 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (~$lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 54, 15])).
% 0.20/0.40 tff(57,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 ($lesseq(b, 0) | (~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(a, 0) | $greatereq(c, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[58, 50, 5, 13, 57])).
% 0.20/0.40 tff(60,plain,($greatereq(c, 0) | (~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(b, 0) | $lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ($greatereq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 41, 13, 56])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (~$lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 61, 39])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((~$lesseq($product(a, $product(b, $product(b, c))), 0)) | $lesseq(b, 0) | $lesseq(c, 0) | $lesseq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[63, 37, 62, 13, 56])).
% 0.20/0.40 tff(65,plain,(((c = 0) | (b = 0) | (a = 0)) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 13])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~(b = 0)) | $lesseq(b, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (~(b = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[67, 13])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~((c = 0) | (b = 0) | (a = 0))) | (c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (a = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 7, 68, 66])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ($greatereq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~($product(a, $product(b, $product(b, c))) = 0)) <=> (~(0 = $product(a, $product(b, $product(b, c)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~($product(a, $product(b, $product(b, c))) = 0)) | (~((c = 0) | (b = 0) | (a = 0))) | (~((~($product(a, $product(b, $product(b, c))) = 0)) <=> ((c = 0) | (b = 0) | (a = 0))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ((~($product(a, $product(b, $product(b, c))) = 0)) | (~((c = 0) | (b = 0) | (a = 0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 31])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[74, 66])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[75, 72])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 ((~(a = 0)) | $lesseq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ($lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 70])).
% 0.20/0.40 tff(79,assumption,(~$greatereq($product(a, $product(b, $product(b, c))), 0)), introduced(assumption)).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ($lesseq(b, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0) | (~$lesseq(a, 0)) | $greatereq(c, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[80, 79, 5, 13, 78])).
% 0.20/0.40 tff(82,plain,($greatereq($product(a, $product(b, $product(b, c))), 0) | $greatereq(c, 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[82, 5, 13])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((0 = $product(a, $product(b, $product(b, c)))) | (~$lesseq($product(a, $product(b, $product(b, c))), 0)) | (~$greatereq($product(a, $product(b, $product(b, c))), 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~$lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 83, 76])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0) | (~$greatereq(a, 0)) | $greatereq(c, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[86, 85, 5, 13, 71])).
% 0.20/0.40 tff(88,plain,($greatereq(c, 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 ($greatereq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[88, 13])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (c = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 9, 68, 66])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~(c = 0)) | $lesseq(c, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ($lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ($lesseq(b, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0) | (~$lesseq(c, 0)) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[93, 79, 92, 13, 3])).
% 0.20/0.40 tff(95,plain,($greatereq(a, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ($greatereq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 79, 13])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ($lesseq(b, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0) | $lesseq(a, 0) | (~$greatereq(c, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 79, 89, 13, 57])).
% 0.20/0.40 tff(99,plain,($lesseq(a, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ($lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[99, 79, 13])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[101, 79, 100, 96])).
% 0.20/0.40 tff(103,plain,($greatereq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[103, 13])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (~$lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 104, 76])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0) | (~$greatereq(c, 0)) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[106, 105, 89, 13, 3])).
% 0.20/0.40 tff(108,plain,($greatereq(a, 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ($greatereq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[108, 13])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (~(a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 57])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (c = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 110, 68, 66])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 ($lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[91, 111])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | $lesseq(b, 0) | (~$lesseq(c, 0)) | $lesseq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[113, 105, 112, 13, 57])).
% 0.20/0.40 tff(115,plain,($lesseq(a, 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 ($lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[115, 13])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[117, 105, 116, 109])).
% 0.20/0.40 tff(119,plain,($lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ((b = 0) | (~$lesseq(b, 0)) | (~$greatereq(b, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 ((b = 0) | (~$greatereq(b, 0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 (~$greatereq(b, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[121, 12])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 ((~$lesseq($product(a, $product(b, $product(b, c))), 0)) | $greatereq(c, 0) | $greatereq(b, 0) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[123, 37, 5, 122, 3])).
% 0.20/0.40 tff(125,plain,(((c = 0) | (b = 0) | (a = 0)) | $greatereq(c, 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[125, 5, 3])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 (b = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 126, 9, 7])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 ((~(b = 0)) | $greatereq(b, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 ($greatereq(b, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.40 tff(130,assumption,($greatereq(b, 0)), introduced(assumption)).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 ((~$lesseq(b, 0)) | (~$greatereq(b, 0)) | $greatereq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[131, 79, 119, 130])).
% 0.20/0.40 tff(133,plain,((~$greatereq(b, 0)) | $greatereq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 (~$greatereq(b, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[133, 79])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 ((~(0 = $product(a, $product(b, $product(b, c))))) <=> (~($product(a, $product(b, $product(b, c))) = 0))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 79])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 137])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (~(b = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[128, 134])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (c = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 9, 139, 138])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 ($lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[91, 140])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0) | $greatereq(b, 0) | (~$lesseq(c, 0)) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[142, 79, 141, 134, 3])).
% 0.20/0.40 tff(144,plain,($greatereq(a, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 ($greatereq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[144, 79])).
% 0.20/0.40 tff(146,plain,
% 0.20/0.40 (c = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 110, 139, 138])).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 ($greatereq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[6, 146])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 ($greatereq($product(a, $product(b, $product(b, c))), 0) | $greatereq(b, 0) | $lesseq(a, 0) | (~$greatereq(c, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[148, 79, 147, 134, 57])).
% 0.20/0.40 tff(150,plain,($lesseq(a, 0) | $greatereq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 ($lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[150, 79])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[101, 79, 151, 145])).
% 0.20/0.40 tff(153,plain,($greatereq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[74, 126])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[154, 72])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 (~$lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 155, 153])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 ((~$lesseq(b, 0)) | $lesseq($product(a, $product(b, $product(b, c))), 0) | (~$greatereq(b, 0)) | $greatereq(c, 0) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(158,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[157, 156, 5, 119, 129, 3])).
% 0.20/0.40 tff(159,plain,($greatereq(c, 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(160,plain,
% 0.20/0.40 ($greatereq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[159, 3])).
% 0.20/0.40 tff(161,plain,
% 0.20/0.40 (~$lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 39, 160])).
% 0.20/0.40 tff(162,plain,
% 0.20/0.40 ((~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $greatereq(b, 0) | $lesseq(c, 0) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(163,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[162, 153, 161, 122, 3])).
% 0.20/0.40 tff(164,plain,(((c = 0) | (b = 0) | (a = 0)) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(165,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[164, 3])).
% 0.20/0.40 tff(166,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[74, 165])).
% 0.20/0.40 tff(167,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[166, 72])).
% 0.20/0.40 tff(168,plain,
% 0.20/0.40 (~$lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 167, 153])).
% 0.20/0.40 tff(169,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | $greatereq(b, 0) | (~$greatereq(c, 0)) | $greatereq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(170,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[169, 168, 160, 4, 3])).
% 0.20/0.40 tff(171,plain,($greatereq(b, 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(172,plain,
% 0.20/0.40 ($greatereq(b, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[171, 3])).
% 0.20/0.40 tff(173,plain,
% 0.20/0.40 ((~$lesseq(b, 0)) | $lesseq($product(a, $product(b, $product(b, c))), 0) | (~$greatereq(b, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(174,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[173, 168, 119, 172])).
% 0.20/0.40 tff(175,plain,($greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(176,assumption,($lesseq(a, 0)), introduced(assumption)).
% 0.20/0.40 tff(177,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[117, 2, 176, 175])).
% 0.20/0.40 tff(178,plain,((~$lesseq(a, 0)) | $lesseq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(179,plain,
% 0.20/0.40 (~$lesseq(a, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[178, 2])).
% 0.20/0.40 tff(180,plain,
% 0.20/0.40 (b = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[121, 130])).
% 0.20/0.40 tff(181,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[11, 180])).
% 0.20/0.40 tff(182,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[74, 181])).
% 0.20/0.40 tff(183,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[182, 72])).
% 0.20/0.40 tff(184,plain,
% 0.20/0.40 (~$lesseq($product(a, $product(b, $product(b, c))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 183, 153])).
% 0.20/0.40 tff(185,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[173, 184, 119, 130])).
% 0.20/0.40 tff(186,plain,(~$greatereq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(187,plain,
% 0.20/0.40 (~(a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[77, 179])).
% 0.20/0.40 tff(188,plain,
% 0.20/0.40 (~(0 = $product(a, $product(b, $product(b, c))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[36, 2])).
% 0.20/0.40 tff(189,plain,
% 0.20/0.40 (~($product(a, $product(b, $product(b, c))) = 0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[188, 135])).
% 0.20/0.40 tff(190,plain,
% 0.20/0.40 ((c = 0) | (b = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 189])).
% 0.20/0.40 tff(191,plain,
% 0.20/0.40 (~(b = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[128, 186])).
% 0.20/0.40 tff(192,plain,
% 0.20/0.40 ((~((c = 0) | (b = 0) | (a = 0))) | (c = 0) | (a = 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 191])).
% 0.20/0.40 tff(193,plain,
% 0.20/0.40 (c = 0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[192, 190, 187])).
% 0.20/0.40 tff(194,plain,
% 0.20/0.40 ($lesseq(c, 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[91, 193])).
% 0.20/0.40 tff(195,plain,
% 0.20/0.40 ($lesseq($product(a, $product(b, $product(b, c))), 0) | $greatereq(b, 0) | (~$lesseq(c, 0)) | $lesseq(a, 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(196,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[195, 2, 194, 186, 179])).
% 0.20/0.40 tff(197,plain,($lesseq($product(a, $product(b, $product(b, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(198,plain,
% 0.20/0.40 ((0 = $product(a, $product(b, $product(b, c)))) | (~$lesseq($product(a, $product(b, $product(b, c))), 0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 153])).
% 0.20/0.40 tff(199,plain,
% 0.20/0.40 (0 = $product(a, $product(b, $product(b, c)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.41 tff(200,plain,
% 0.20/0.41 ($product(a, $product(b, $product(b, c))) = 0),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[199, 1])).
% 0.20/0.41 tff(201,plain,
% 0.20/0.41 (~((c = 0) | (b = 0) | (a = 0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[74, 200])).
% 0.20/0.41 tff(202,plain,
% 0.20/0.41 (~(a = 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[14, 201])).
% 0.20/0.41 tff(203,plain,
% 0.20/0.41 ((a = 0) | (~$lesseq(a, 0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 175])).
% 0.20/0.41 tff(204,plain,
% 0.20/0.41 (~$lesseq(a, 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.41 tff(205,plain,
% 0.20/0.41 (~(c = 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 201])).
% 0.20/0.41 tff(206,plain,
% 0.20/0.41 ((~$greatereq($product(a, $product(b, $product(b, c))), 0)) | $greatereq(b, 0) | $lesseq(a, 0) | $greatereq(c, 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(207,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[206, 153, 5, 186, 204])).
% 0.20/0.41 tff(208,plain,($greatereq(c, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(209,plain,
% 0.20/0.41 (~$lesseq(c, 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 208, 205])).
% 0.20/0.41 tff(210,plain,
% 0.20/0.41 ((~$lesseq($product(a, $product(b, $product(b, c))), 0)) | $greatereq(b, 0) | $lesseq(c, 0) | $lesseq(a, 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(211,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[210, 197, 209, 186, 204])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------