TSTP Solution File: ARI672_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI672_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 17:02:32 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ARI672_1 : TPTP v8.1.0. Released v6.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n011.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 01:28:10 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(b_type, type, (
% 0.13/0.39 b: $int)).
% 0.13/0.39 tff(a_type, type, (
% 0.13/0.39 a: $int)).
% 0.13/0.39 tff(1,assumption,(~$greatereq(b, 1)), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(~$greatereq(a, 1)), introduced(assumption)).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~(a = 1)) | $greatereq(a, 1)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~(a = 1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,assumption,(~((~((a = -1) | (a = 1))) | (~(a = b)))), introduced(assumption)).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (((~((a = -1) | (a = 1))) | (~(a = b))) | (a = b)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (a = b),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~(a = b)) | $lesseq($sum(a, $product(-1, b)), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ($lesseq($sum(a, $product(-1, b)), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,assumption,(~(a = 1)), introduced(assumption)).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (((~((a = -1) | (a = 1))) | (~(a = b))) | ((a = -1) | (a = 1))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((a = -1) | (a = 1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 5])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~((a = -1) | (a = 1))) | (a = -1) | (a = 1)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (a = -1),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[13, 12, 10])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 ((~(a = -1)) | $greatereq(a, -1)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ($greatereq(a, -1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((~(a = -1)) | $lesseq(a, -1)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ($lesseq(a, -1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (((~($product(a, b) = 1)) <=> (~((~((a = -1) | (a = 1))) | (~(a = b))))) <=> (($product(a, b) = 1) <=> ((~((a = -1) | (a = 1))) | (~(a = b))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((((a = -1) | (a = 1)) & (a = b)) <=> (~((~((a = -1) | (a = 1))) | (~(a = b))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b))) <=> ((~($product(a, b) = 1)) <=> (~((~((a = -1) | (a = 1))) | (~(a = b)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b))) <=> (($product(a, b) = 1) <=> ((~((a = -1) | (a = 1))) | (~(a = b))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[21, 19])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b))) <=> ((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~(($product(a, b) = 1) <=> (((a = -1) | (a = 1)) & (a = b)))) <=> ((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(25,axiom,(~(($product(a, b) = 1) <=> (((a = -1) | (a = 1)) & (a = b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) <=> (((a = -1) | (a = 1)) & (a = b))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (($product(a, b) = 1) <=> ((~((a = -1) | (a = 1))) | (~(a = b)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) | ((~((a = -1) | (a = 1))) | (~(a = b))) | (~(($product(a, b) = 1) <=> ((~((a = -1) | (a = 1))) | (~(a = b)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) | ((~((a = -1) | (a = 1))) | (~(a = b)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (~($product(a, b) = 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 5])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~(a = b)) | $greatereq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ($greatereq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 7])).
% 0.13/0.40 tff(34,assumption,($greatereq($sum(a, $product(-1, b)), 0)), introduced(assumption)).
% 0.13/0.40 tff(35,assumption,($greatereq(b, 0)), introduced(assumption)).
% 0.13/0.40 tff(36,assumption,($lesseq(a, -1)), introduced(assumption)).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[36, 35, 34])).
% 0.13/0.40 tff(38,plain,((~$greatereq(b, 0)) | (~$lesseq(a, -1)) | (~$greatereq($sum(a, $product(-1, b)), 0))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (~$greatereq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[38, 18, 33])).
% 0.13/0.40 tff(40,assumption,(~$greatereq(b, 0)), introduced(assumption)).
% 0.13/0.40 tff(41,assumption,(~$greatereq($product(a, b), 1)), introduced(assumption)).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ($greatereq(b, 0) | $greatereq($product(a, b), 1) | (~$lesseq(a, -1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[42, 41, 36, 40])).
% 0.13/0.40 tff(44,plain,($greatereq($product(a, b), 1) | (~$lesseq(a, -1)) | $greatereq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ($greatereq($product(a, b), 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[44, 18, 39])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (($product(a, b) = 1) | (~$lesseq($product(a, b), 1)) | (~$greatereq($product(a, b), 1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (~$lesseq($product(a, b), 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 45, 31])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ($lesseq(b, -2) | $lesseq($product(a, b), 1) | (~$lesseq(a, -1)) | (~$greatereq(a, -1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ($lesseq(b, -2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[48, 47, 18, 16])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[16, 49, 9])).
% 0.13/0.40 tff(51,plain,(((~((a = -1) | (a = 1))) | (~(a = b))) | (a = 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~((a = -1) | (a = 1))) | (~(a = b))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 4])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (($product(a, b) = 1) | (~((~((a = -1) | (a = 1))) | (~(a = b)))) | (~(($product(a, b) = 1) <=> ((~((a = -1) | (a = 1))) | (~(a = b)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (($product(a, b) = 1) | (~((~((a = -1) | (a = 1))) | (~(a = b))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 28])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ($product(a, b) = 1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 52])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) | $lesseq($product(a, b), 1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 ($lesseq($product(a, b), 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((~($product(a, b) = 1)) | $greatereq($product(a, b), 1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 ($greatereq($product(a, b), 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.13/0.40 tff(60,assumption,($lesseq($product(a, b), 1)), introduced(assumption)).
% 0.13/0.40 tff(61,assumption,(~$greatereq(a, -1)), introduced(assumption)).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 ($greatereq(b, 0) | (~$lesseq($product(a, b), 1)) | $greatereq(a, -1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[62, 60, 61, 40])).
% 0.13/0.40 tff(64,plain,($greatereq(b, 0) | (~$lesseq($product(a, b), 1)) | $greatereq(a, -1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ($greatereq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 0.13/0.40 tff(66,assumption,($greatereq($product(a, b), 1)), introduced(assumption)).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 ((~$greatereq(b, 0)) | (~$greatereq($product(a, b), 1)) | $greatereq(a, -1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[67, 66, 61, 65])).
% 0.13/0.40 tff(69,plain,($greatereq(a, -1) | (~$greatereq($product(a, b), 1)) | (~$lesseq($product(a, b), 1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(70,plain,
% 0.13/0.40 ($greatereq(a, -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[69, 59, 57])).
% 0.13/0.40 tff(71,assumption,(~$lesseq(a, -1)), introduced(assumption)).
% 0.13/0.40 tff(72,plain,
% 0.13/0.40 ((~$greatereq($product(a, b), 1)) | $greatereq(a, 1) | $lesseq(a, -1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(73,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[72, 59, 71, 2])).
% 0.13/0.40 tff(74,plain,($lesseq(a, -1) | $greatereq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(75,plain,
% 0.13/0.40 ($lesseq(a, -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[74, 2])).
% 0.13/0.40 tff(76,plain,
% 0.13/0.40 ((a = -1) | (~$lesseq(a, -1)) | (~$greatereq(a, -1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(77,plain,
% 0.13/0.40 (a = -1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[76, 70, 75])).
% 0.13/0.40 tff(78,plain,
% 0.13/0.40 (((a = -1) | (a = 1)) | (~(a = -1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(79,plain,
% 0.13/0.40 ((a = -1) | (a = 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.13/0.40 tff(80,plain,
% 0.13/0.40 ((~((~((a = -1) | (a = 1))) | (~(a = b)))) | (~((a = -1) | (a = 1))) | (~(a = b))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(81,plain,
% 0.13/0.40 (~(a = b)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[80, 79, 52])).
% 0.13/0.40 tff(82,assumption,(~$lesseq($sum(a, $product(-1, b)), 0)), introduced(assumption)).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 ($greatereq(b, -1) | (~$lesseq($product(a, b), 1)) | (~$lesseq(a, -1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 ($greatereq(b, -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[83, 60, 36])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[36, 84, 82])).
% 0.13/0.40 tff(86,plain,($lesseq($sum(a, $product(-1, b)), 0) | (~$lesseq(a, -1)) | (~$lesseq($product(a, b), 1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 ($lesseq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[86, 75, 57])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 ((a = b) | (~$lesseq($sum(a, $product(-1, b)), 0)) | (~$greatereq($sum(a, $product(-1, b)), 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (~$greatereq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[88, 87, 81])).
% 0.13/0.40 tff(90,assumption,(~$greatereq($sum(a, $product(-1, b)), 0)), introduced(assumption)).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 ($lesseq(b, -1) | $greatereq(b, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ($lesseq(b, -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[91, 40])).
% 0.13/0.40 tff(93,assumption,($greatereq(a, -1)), introduced(assumption)).
% 0.13/0.40 tff(94,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[93, 92, 90])).
% 0.13/0.40 tff(95,plain,($greatereq($sum(a, $product(-1, b)), 0) | (~$greatereq(a, -1)) | $greatereq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(96,plain,
% 0.13/0.40 ($greatereq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[95, 89, 70])).
% 0.13/0.40 tff(97,plain,
% 0.13/0.40 ((~$lesseq(b, -1)) | (~$greatereq(b, 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(98,plain,
% 0.13/0.40 (~$lesseq(b, -1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.13/0.40 tff(99,plain,
% 0.13/0.40 ($lesseq(b, -1) | (~$greatereq($product(a, b), 1)) | (~$lesseq(a, -1)) | (~$greatereq(a, -1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(100,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[99, 59, 75, 70, 98])).
% 0.13/0.40 tff(101,plain,($greatereq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(102,assumption,(~$lesseq(a, 1)), introduced(assumption)).
% 0.13/0.40 tff(103,assumption,($lesseq(b, 0)), introduced(assumption)).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 (~($product(a, b) = 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 41])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (~((~((a = -1) | (a = 1))) | (~(a = b)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 104])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (a = b),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[6, 105])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 ($lesseq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 106])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (a = 1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 105])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 ((~(a = 1)) | $lesseq(a, 1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(110,plain,
% 0.13/0.40 ($lesseq(a, 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 ($lesseq(b, 0) | (~$lesseq(a, 1)) | (~$greatereq(a, 1)) | $greatereq($product(a, b), 1)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(112,plain,
% 0.13/0.40 ($lesseq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[111, 41, 110, 101])).
% 0.13/0.40 tff(113,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[101, 112, 107])).
% 0.13/0.40 tff(114,plain,($greatereq($product(a, b), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 ($lesseq(a, 1) | (~$greatereq($product(a, b), 1)) | (~$lesseq(b, 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[115, 114, 102, 103])).
% 0.13/0.40 tff(117,plain,((~$lesseq(b, 0)) | $lesseq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(118,plain,
% 0.13/0.40 (~$lesseq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[117, 102])).
% 0.13/0.40 tff(119,assumption,(~$lesseq($product(a, b), 1)), introduced(assumption)).
% 0.13/0.40 tff(120,plain,
% 0.13/0.40 (~($product(a, b) = 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 119])).
% 0.13/0.40 tff(121,plain,
% 0.13/0.40 (~((~((a = -1) | (a = 1))) | (~(a = b)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[54, 120])).
% 0.13/0.40 tff(122,plain,
% 0.13/0.40 (a = b),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[6, 121])).
% 0.13/0.40 tff(123,plain,
% 0.13/0.40 ($greatereq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 122])).
% 0.13/0.40 tff(124,plain,
% 0.13/0.40 (a = 1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 121])).
% 0.13/0.40 tff(125,plain,
% 0.13/0.40 ($lesseq(a, 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[109, 124])).
% 0.13/0.40 tff(126,plain,
% 0.13/0.40 ($greatereq(b, 2) | (~$lesseq(a, 1)) | $lesseq($product(a, b), 1) | (~$greatereq(a, 1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(127,plain,
% 0.13/0.40 ($greatereq(b, 2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[126, 119, 125, 101])).
% 0.13/0.40 tff(128,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[125, 127, 123])).
% 0.13/0.40 tff(129,plain,($lesseq($product(a, b), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(130,plain,
% 0.13/0.40 ((~$lesseq($product(a, b), 1)) | $lesseq(a, 1) | $lesseq(b, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(131,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[130, 129, 102, 118])).
% 0.13/0.40 tff(132,plain,($lesseq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(133,plain,
% 0.13/0.40 ($greatereq(b, 1) | (~$lesseq(a, 1)) | (~$greatereq($product(a, b), 1)) | (~$greatereq(a, 1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(134,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[133, 114, 132, 101, 1])).
% 0.13/0.40 tff(135,plain,($greatereq(b, 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(136,plain,
% 0.13/0.40 ($lesseq(b, 1) | (~$lesseq($product(a, b), 1)) | (~$greatereq(a, 1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(137,plain,
% 0.13/0.40 ($lesseq(b, 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[136, 129, 101])).
% 0.13/0.40 tff(138,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[101, 137, 90])).
% 0.13/0.40 tff(139,plain,($greatereq($sum(a, $product(-1, b)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(140,plain,
% 0.13/0.40 ($product(a, b) = 1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 114, 129])).
% 0.13/0.40 tff(141,plain,
% 0.13/0.40 ((~((a = -1) | (a = 1))) | (~(a = b))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 140])).
% 0.13/0.40 tff(142,plain,
% 0.13/0.40 ((a = 1) | (~$lesseq(a, 1)) | (~$greatereq(a, 1))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(143,plain,
% 0.13/0.40 ((a = 1) | (~$lesseq(a, 1))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[142, 101])).
% 0.13/0.40 tff(144,plain,
% 0.13/0.40 (a = 1),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[143, 132])).
% 0.13/0.40 tff(145,plain,
% 0.13/0.40 (((a = -1) | (a = 1)) | (~(a = 1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(146,plain,
% 0.13/0.40 ((a = -1) | (a = 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.13/0.40 tff(147,plain,
% 0.13/0.40 (~(a = b)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[80, 146, 141])).
% 0.13/0.40 tff(148,plain,
% 0.13/0.40 (~$lesseq($sum(a, $product(-1, b)), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[88, 147, 139])).
% 0.13/0.40 tff(149,plain,
% 0.13/0.40 ((~$lesseq(a, 1)) | $lesseq($sum(a, $product(-1, b)), 0) | $lesseq(b, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(150,plain,
% 0.13/0.40 ($lesseq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[149, 148, 132])).
% 0.13/0.40 tff(151,plain,
% 0.13/0.40 ((~$greatereq(b, 1)) | (~$lesseq(b, 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(152,plain,
% 0.13/0.40 (~$greatereq(b, 1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.13/0.40 tff(153,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[152, 135])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------