TSTP Solution File: ARI656_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI656_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 17:02:28 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI656_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 : n028.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 01:29:48 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $int)).
% 0.19/0.39 tff(b_type, type, (
% 0.19/0.39 b: $int)).
% 0.19/0.39 tff(c_type, type, (
% 0.19/0.39 c: $int)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 ((~$lesseq($product(a, c), $product(a, b))) <=> (~$lesseq($sum($product(c, a), $product(-1, $product(b, a))), 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 ((~$lesseq($product(a, c), $product(a, b))) <=> (~$lesseq($product(a, c), $product(a, b)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(3,axiom,(~$lesseq($product(a, c), $product(a, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_002')).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (~$lesseq($product(a, c), $product(a, b))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (~$lesseq($sum($product(c, a), $product(-1, $product(b, a))), 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.39 tff(6,assumption,(~$lesseq($product(c, a), 0)), introduced(assumption)).
% 0.19/0.39 tff(7,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ($lesseq(c, b) <=> $lesseq($sum(c, $product(-1, b)), 0)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ($lesseq(c, b) <=> $lesseq(c, b)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(10,axiom,($lesseq(c, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ($lesseq(c, b)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ($lesseq($sum(c, $product(-1, b)), 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((0 = $sum($product(b, a), $product(-1, b))) <=> ($sum($product(b, a), $product(-1, b)) = 0)),
% 0.19/0.39 inference(commutativity,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (($sum($product(b, a), $product(-1, b)) = 0) <=> (0 = $sum($product(b, a), $product(-1, b)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[13])).
% 0.19/0.39 tff(15,assumption,(~$lesseq(a, 1)), introduced(assumption)).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~$lesseq($sum(c, $product(-1, b)), 0)) | $lesseq($sum($product(c, a), $product(-1, $product(b, a))), 0) | $lesseq(a, 1)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[16, 12, 5, 15])).
% 0.19/0.39 tff(18,plain,($lesseq(a, 1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (($sum($product(b, a), $product(-1, b)) = 0) | $lesseq(a, 0) | (~$lesseq(a, 1))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ($sum($product(b, a), $product(-1, b)) = 0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 7, 18])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (0 = $sum($product(b, a), $product(-1, b))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~(0 = $sum($product(b, a), $product(-1, b)))) | $greatereq($sum($product(b, a), $product(-1, b)), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ($greatereq($sum($product(b, a), $product(-1, b)), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,assumption,($lesseq($sum($product(c, a), $product(-1, c)), 0)), introduced(assumption)).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[24, 5, 23, 12])).
% 0.19/0.39 tff(26,plain,((~$lesseq($sum($product(c, a), $product(-1, c)), 0)) | $lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (~$lesseq($sum($product(c, a), $product(-1, c)), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ($lesseq(a, 0) | (~$lesseq(a, 1)) | $lesseq($sum($product(c, a), $product(-1, c)), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[28, 7, 18, 27])).
% 0.19/0.39 tff(30,plain,($lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ($lesseq(0, a) <=> $greatereq(a, 0)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 ($lesseq(0, a) <=> $lesseq(0, a)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(33,axiom,($lesseq(0, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_001')).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ($lesseq(0, a)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ($greatereq(a, 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ($lesseq($product(c, a), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 35, 30, 6])).
% 0.19/0.39 tff(38,plain,($lesseq($product(c, a), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~$greatereq($product(b, a), 0)) | $lesseq($sum($product(c, a), $product(-1, $product(b, a))), 0) | (~$lesseq($product(c, a), 0))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~$greatereq($product(b, a), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38, 5])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((~$greatereq(b, 0)) | (~$lesseq(a, 0)) | $greatereq($product(b, a), 0) | (~$greatereq(a, 0))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~$greatereq(b, 0)) | (~$lesseq(a, 0)) | $greatereq($product(b, a), 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[41, 35])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (~$greatereq(b, 0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 40, 30])).
% 0.19/0.39 tff(44,assumption,(~$greatereq($product(b, a), 0)), introduced(assumption)).
% 0.19/0.39 tff(45,assumption,(~$greatereq(b, 0)), introduced(assumption)).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 ((~$lesseq(a, 0)) | $greatereq($product(b, a), 0) | $greatereq(b, 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45, 30, 44])).
% 0.19/0.39 tff(48,plain,($greatereq($product(b, a), 0) | $greatereq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 43, 40])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------