TSTP Solution File: ARI668_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI668_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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
% 0.03/0.12 % Problem : ARI668_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 01:29:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(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: $int)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (($sum($product(11, a), $product(7, b)) = 1) <=> ($sum($product(11, a), $product(7, b)) = 1)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,axiom,($sum($product(11, a), $product(7, b)) = 1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 ($sum($product(11, a), $product(7, b)) = 1),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~($sum($product(11, a), $product(7, b)) = 1)) | $lesseq($sum($product(11, a), $product(7, b)), 1)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ($lesseq($sum($product(11, a), $product(7, b)), 1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,assumption,($lesseq(a, -2)), introduced(assumption)).
% 0.20/0.39 tff(7,assumption,($lesseq(a, -4)), introduced(assumption)).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~($sum($product(11, a), $product(7, b)) = 1)) | $greatereq($sum($product(11, a), $product(7, b)), 1)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ($greatereq($sum($product(11, a), $product(7, b)), 1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 3])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ($lesseq(a, c) <=> $lesseq($sum(a, $product(-1, c)), 0)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ($lesseq(a, c) <=> $lesseq(a, c)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(12,axiom,($lesseq(a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_001')).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ($lesseq(a, c)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ($lesseq($sum(a, $product(-1, c)), 0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.39 tff(15,assumption,(~$greatereq(c, 0)), introduced(assumption)).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ($greatereq(c, 0) | (~$lesseq($sum(a, $product(-1, c)), 0)) | (~$greatereq(a, 0))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~$greatereq(a, 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[16, 15, 14])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 ((~$lesseq($sum($product(11, a), $product(7, b)), 1)) | (~$greatereq($sum($product(11, a), $product(7, b)), 1)) | $greatereq(a, 0) | $lesseq(a, -3)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ($lesseq(a, -3)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[18, 17, 9, 5])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ($lesseq(a, -2) | (~$lesseq(a, -3))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ($lesseq(a, -2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.39 tff(22,assumption,($lesseq(b, -3)), introduced(assumption)).
% 0.20/0.39 tff(23,assumption,(~$greatereq(a, 2)), introduced(assumption)).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[9, 22, 23])).
% 0.20/0.39 tff(25,plain,($greatereq(a, 2) | (~$lesseq(b, -3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ($greatereq(a, 2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.20/0.39 tff(27,assumption,($lesseq(c, 0)), introduced(assumption)).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[22, 9, 14, 27])).
% 0.20/0.39 tff(29,plain,((~$lesseq(c, 0)) | (~$lesseq(b, -3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (~$lesseq(c, 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[29, 22])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~$greatereq(a, 2)) | $greatereq($sum($product(a, c), $product(-2, c)), 0) | $lesseq(c, 0)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~$greatereq(a, 2)) | $greatereq($sum($product(a, c), $product(-2, c)), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ($greatereq($sum($product(a, c), $product(-2, c)), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 26])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~$lesseq(4, $product(a, c))) <=> (~$greatereq($product(a, c), 4))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~$lesseq(4, $product(a, c))) <=> (~$lesseq(4, $product(a, c)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(36,axiom,(~($lesseq(4, $product(a, c)) | $greatereq(0, $product(a, c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_002')).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (~$lesseq(4, $product(a, c))),
% 0.20/0.39 inference(or_elim,[status(thm)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (~$lesseq(4, $product(a, c))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (~$greatereq($product(a, c), 4)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[26, 14, 39, 33])).
% 0.20/0.39 tff(41,plain,(~$lesseq(b, -3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~$lesseq($sum($product(11, a), $product(7, b)), 1)) | (~$greatereq($sum($product(11, a), $product(7, b)), 1)) | $greatereq(b, 0) | $lesseq(b, -3)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ($greatereq(b, 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[42, 41, 9, 5])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ($greatereq(c, 0) | (~$lesseq(a, -4)) | $greatereq($product(a, c), 4)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 39, 15, 7])).
% 0.20/0.40 tff(46,plain,((~$lesseq(a, -4)) | $greatereq(c, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (~$lesseq(a, -4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 15])).
% 0.20/0.40 tff(48,assumption,(~$lesseq(a, -4)), introduced(assumption)).
% 0.20/0.40 tff(49,assumption,(~$lesseq(b, 4)), introduced(assumption)).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[5, 49, 48])).
% 0.20/0.40 tff(51,plain,($lesseq(a, -4) | $lesseq(b, 4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 ($lesseq(b, 4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 ((~$greatereq(b, 5)) | (~$lesseq(b, 4))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (~$greatereq(b, 5)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 ((~$lesseq($sum($product(11, a), $product(7, b)), 1)) | $greatereq(b, 5) | (~$greatereq(b, 0)) | (~$greatereq($sum($product(11, a), $product(7, b)), 1)) | $lesseq(b, 2)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ($lesseq(b, 2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 54, 43, 9, 5])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[9, 56, 21])).
% 0.20/0.40 tff(58,plain,($greatereq(c, 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~$greatereq(0, $product(a, c))) <=> (~$lesseq($product(a, c), 0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~$greatereq(0, $product(a, c))) <=> (~$greatereq(0, $product(a, c)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (~$greatereq(0, $product(a, c))),
% 0.20/0.40 inference(or_elim,[status(thm)],[36])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (~$greatereq(0, $product(a, c))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (~$lesseq($product(a, c), 0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~$lesseq(a, -4)) | $lesseq($product(a, c), 0) | (~$greatereq(c, 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[64, 63, 58, 7])).
% 0.20/0.40 tff(66,plain,(~$lesseq(a, -4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ($lesseq(b, 4)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[51, 66])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (~$greatereq(b, 5)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ($greatereq(b, 5) | $lesseq(b, 2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 43, 9, 5])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ($lesseq(b, 2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[9, 70, 6])).
% 0.20/0.40 tff(72,plain,(~$lesseq(a, -2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ((~$lesseq($sum($product(11, a), $product(7, b)), 1)) | (~$greatereq($sum($product(11, a), $product(7, b)), 1)) | $lesseq(a, -2) | $greatereq(a, 1)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 ($greatereq(a, 1)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[73, 9, 72, 5])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[5, 43, 74])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------