TSTP Solution File: ARI652_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI652_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 17:02:27 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
% 0.12/0.12 % Problem : ARI652_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 : n011.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 01:14:55 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(a_type, type, (
% 0.13/0.39 a: $int)).
% 0.13/0.39 tff(1,assumption,(~$greatereq($product(a, a), 1)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ($lesseq(a, -1) <=> $lesseq(a, -1)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ($lesseq(-2, $sum(-3, $product(-1, a))) <=> $lesseq(a, -1)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ($difference(-3, a) = $sum(-3, $product(-1, a))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ($lesseq(-2, $difference(-3, a)) <=> $lesseq(-2, $sum(-3, $product(-1, a)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 ($lesseq(-2, $difference(-3, a)) <=> $lesseq(a, -1)),
% 0.13/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,axiom,($lesseq(-2, $difference(-3, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_001')).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ($lesseq(a, -1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ($lesseq(a, -1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~$lesseq(a, -1)) | $greatereq($product(a, a), 1)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[10, 9, 1])).
% 0.13/0.39 tff(12,plain,($greatereq($product(a, a), 1)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~($product(a, a) = 1)) <=> (~($product(a, a) = 1))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,axiom,(~($product(a, a) = 1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_002')).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~($product(a, a) = 1)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (($product(a, a) = 1) | (~$lesseq($product(a, a), 1)) | (~$greatereq($product(a, a), 1))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((~$lesseq($product(a, a), 1)) | (~$greatereq($product(a, a), 1))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (~$lesseq($product(a, a), 1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~$lesseq(a, -2)) <=> (~$lesseq(a, -2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~$lesseq($sum(4, a), 2)) <=> (~$lesseq(a, -2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ($less(2, $sum(4, a)) <=> (~$lesseq($sum(4, a), 2))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ($sum(a, 4) = $sum(4, a)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ($less(2, $sum(a, 4)) <=> $less(2, $sum(4, a))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ($less(2, $sum(a, 4)) <=> (~$lesseq($sum(4, a), 2))),
% 0.13/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ($less(2, $sum(a, 4)) <=> (~$lesseq(a, -2))),
% 0.13/0.39 inference(transitivity,[status(thm)],[24, 20])).
% 0.13/0.39 tff(26,axiom,($less(2, $sum(a, 4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~$lesseq(a, -2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~$lesseq(a, -2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ($lesseq(a, -2) | (~$lesseq(a, -1)) | $lesseq($product(a, a), 1)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28, 9, 18])).
% 0.13/0.39 % SZS output end Proof
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