TSTP Solution File: ARI682_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI682_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 17:02:35 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ARI682_1 : TPTP v8.1.0. Released v6.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 01:40:20 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(b_type, type, (
% 0.13/0.38 b: $int)).
% 0.13/0.38 tff(a_type, type, (
% 0.13/0.38 a: $int)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 ((~$lesseq(b, a)) <=> (~$greatereq($sum(a, $product(-1, b)), 0))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~$lesseq(b, a)) <=> (~$lesseq(b, a))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ($less(a, b) <=> (~$lesseq(b, a))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(4,axiom,($less(a, b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~$lesseq(b, a)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (~$lesseq(b, a)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~$greatereq($sum(a, $product(-1, b)), 0)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ($lesseq(0, a) <=> $greatereq(a, 0)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 ($lesseq(0, a) <=> $lesseq(0, a)),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(10,axiom,($lesseq(0, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_001')).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ($lesseq(0, a)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ($greatereq(a, 0)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.13/0.38 tff(13,assumption,($greatereq($product(a, b), 0)), introduced(assumption)).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 ((~$lesseq(a, $sum(-1, $sum($product(a, b), b)))) <=> (~$lesseq($sum(a, $sum($product(-1, b), $product(-1, $product(a, b)))), -1))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 ((~$lesseq(a, $sum(-1, $sum($product(a, b), b)))) <=> (~$lesseq(a, $sum(-1, $sum($product(a, b), b))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 ((~$lesseq($sum(a, 1), $sum($product(a, b), b))) <=> (~$lesseq(a, $sum(-1, $sum($product(a, b), b))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(17,axiom,(~$lesseq($sum(a, 1), $sum($product(a, b), b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_002')).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (~$lesseq(a, $sum(-1, $sum($product(a, b), b)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (~$lesseq(a, $sum(-1, $sum($product(a, b), b)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (~$lesseq($sum(a, $sum($product(-1, b), $product(-1, $product(a, b)))), -1)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(theory_lemma,[status(thm)],[20, 7, 13])).
% 0.13/0.38 tff(22,plain,(~$greatereq($product(a, b), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 ($lesseq(b, 0) | $greatereq($product(a, b), 0) | (~$greatereq(a, 0))),
% 0.13/0.38 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 ($lesseq(b, 0) | $greatereq($product(a, b), 0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 ($lesseq(b, 0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[24, 22])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(theory_lemma,[status(thm)],[25, 12, 7])).
% 0.13/0.38 % SZS output end Proof
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