TSTP Solution File: ARI679_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI679_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 17:02:34 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ARI679_1 : TPTP v8.1.0. Released v6.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.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 01:43:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(c_type, type, (
% 0.20/0.38 c: $int)).
% 0.20/0.38 tff(d_type, type, (
% 0.20/0.38 d: $int)).
% 0.20/0.38 tff(1,assumption,(~$greatereq(c, 3)), introduced(assumption)).
% 0.20/0.38 tff(2,assumption,(~$lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0)), introduced(assumption)).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 ($lesseq(2, c) <=> $greatereq(c, 2)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ($lesseq(2, c) <=> $lesseq(2, c)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,($lesseq(2, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_001')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ($lesseq(2, c)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 ($greatereq(c, 2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ($lesseq(3, d) <=> $greatereq(d, 3)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ($lesseq(3, d) <=> $lesseq(3, d)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(10,axiom,($lesseq(3, d)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ($lesseq(3, d)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ($greatereq(d, 3)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 ($lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0) | (~$greatereq(d, 3)) | (~$greatereq(c, 2))),
% 0.20/0.38 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[13, 12, 7, 2])).
% 0.20/0.38 tff(15,plain,($lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((~$greatereq(c, 2)) | (~$lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0)) | $greatereq($product(d, c), 6)),
% 0.20/0.38 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ($greatereq($product(d, c), 6)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[16, 7, 15])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $sum($product(-3, c), $product(c, d))))) <=> ((~$greatereq($product(d, c), 6)) <=> $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d))))) <=> ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $sum($product(-3, c), $product(c, d)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d))))) <=> ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~($lesseq(6, $product(c, d)) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d)))))) <=> ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (($lesseq($product(2, 3), $product(c, d)) <=> $lesseq($product(2, $difference(d, 3)), $product(c, $difference(d, 3)))) <=> ($lesseq(6, $product(c, d)) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~($lesseq($product(2, 3), $product(c, d)) <=> $lesseq($product(2, $difference(d, 3)), $product(c, $difference(d, 3))))) <=> (~($lesseq(6, $product(c, d)) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~($lesseq($product(2, 3), $product(c, d)) <=> $lesseq($product(2, $difference(d, 3)), $product(c, $difference(d, 3))))) <=> ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.38 tff(25,axiom,(~($lesseq($product(2, 3), $product(c, d)) <=> $lesseq($product(2, $difference(d, 3)), $product(c, $difference(d, 3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_002')).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $product(c, $sum(-3, d))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((~$lesseq(6, $product(c, d))) <=> $lesseq($product(2, d), $sum(6, $sum($product(-3, c), $product(c, d))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~$greatereq($product(d, c), 6)) <=> $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~$greatereq($product(d, c), 6)) | (~$lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)) | (~((~$greatereq($product(d, c), 6)) <=> $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~$greatereq($product(d, c), 6)) | (~$lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~$lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 17])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ($lesseq($sum($product(2, d), $product(-1, $product(d, c))), 0) | (~$greatereq(d, 3)) | (~$greatereq(c, 2))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ($lesseq($sum($product(2, d), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 12, 7])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[34, 32, 1])).
% 0.20/0.39 tff(36,plain,($greatereq(c, 3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(37,assumption,(~$greatereq(c, 4)), introduced(assumption)).
% 0.20/0.39 tff(38,assumption,(~$lesseq($sum($product(4, c), $product(-1, $product(d, c))), 0)), introduced(assumption)).
% 0.20/0.39 tff(39,assumption,(~$greatereq(d, 4)), introduced(assumption)).
% 0.20/0.39 tff(40,assumption,(~$lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)), introduced(assumption)).
% 0.20/0.39 tff(41,assumption,($lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0)), introduced(assumption)).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[41, 40, 39])).
% 0.20/0.39 tff(43,plain,((~$lesseq($sum($product(3, c), $product(-1, $product(d, c))), 0)) | $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6) | $greatereq(d, 4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ($greatereq(d, 4)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 32, 15])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~$greatereq(d, 4)) | $lesseq($sum($product(4, c), $product(-1, $product(d, c))), 0) | (~$greatereq(c, 2))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 7, 44, 38])).
% 0.20/0.39 tff(47,plain,($lesseq($sum($product(4, c), $product(-1, $product(d, c))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(48,assumption,(~$greatereq(d, 5)), introduced(assumption)).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[48, 34, 47, 32])).
% 0.20/0.39 tff(50,plain,($greatereq(d, 5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~$greatereq(d, 5)) | $lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0) | (~$greatereq(c, 2))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~$greatereq(d, 5)) | $lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 7])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ($lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[52, 50])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~$lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0)) | $greatereq(c, 4) | (~$greatereq(c, 3)) | $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 32, 53, 37, 36])).
% 0.20/0.39 tff(56,plain,($greatereq(c, 4)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~$greatereq(c, 4)) | $lesseq($sum($product(4, d), $product(-1, $product(d, c))), 0) | (~$greatereq(d, 5))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~$greatereq(c, 4)) | $lesseq($sum($product(4, d), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 50])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ($lesseq($sum($product(4, d), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 56])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~$lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0)) | $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6) | (~$lesseq($sum($product(4, d), $product(-1, $product(d, c))), 0)) | (~$lesseq($sum($product(10, c), $product(-1, $product(d, c))), 0))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (~$lesseq($sum($product(10, c), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 53, 32, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~$lesseq($sum($product(5, c), $product(-1, $product(d, c))), 0)) | (~$lesseq($sum($product(4, d), $product(-1, $product(d, c))), 0)) | $lesseq($sum($product(2, d), $sum($product(3, c), $product(-1, $product(d, c)))), 6) | $greatereq(d, 10)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ($greatereq(d, 10)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 53, 32, 59])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~$greatereq(d, 10)) | $lesseq($sum($product(10, c), $product(-1, $product(d, c))), 0) | (~$greatereq(c, 2))),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~$greatereq(d, 10)) | $lesseq($sum($product(10, c), $product(-1, $product(d, c))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 7])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 63, 61])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------