TSTP Solution File: ARI643_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI643_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 17:02:25 EDT 2022
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ARI643_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 01:09:40 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(a_type, type, (
% 0.18/0.37 a: $int)).
% 0.18/0.37 tff(1,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ($lesseq(a, 0) | $greatereq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 ($greatereq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 ($lesseq(a, 0) | $lesseq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 ($lesseq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 ((0 = $quotient_e(0, a)) <=> ($quotient_e(0, a) = 0)),
% 0.18/0.37 inference(commutativity,[status(thm)],[])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (($quotient_e(0, a) = 0) <=> (0 = $quotient_e(0, a))),
% 0.18/0.37 inference(symmetry,[status(thm)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~($quotient_e(0, a) = 0)) <=> (~(0 = $quotient_e(0, a)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~($quotient_e(0, a) = 0)) <=> (~($quotient_e(0, a) = 0))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ((~((~(a = 0)) => ($quotient_e(0, a) = 0))) <=> (~((a = 0) | ($quotient_e(0, a) = 0)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(11,axiom,(~((~(a = 0)) => ($quotient_e(0, a) = 0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (~((a = 0) | ($quotient_e(0, a) = 0))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (~($quotient_e(0, a) = 0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[12])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (~($quotient_e(0, a) = 0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (~(0 = $quotient_e(0, a))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 ((0 = $quotient_e(0, a)) | (~$lesseq($quotient_e(0, a), 0)) | (~$greatereq($quotient_e(0, a), 0))),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 ((~$lesseq($quotient_e(0, a), 0)) | (~$greatereq($quotient_e(0, a), 0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[17, 5, 3])).
% 0.18/0.37 tff(19,plain,($lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 ((~(a = 0)) <=> (~(a = 0))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (~(a = 0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[12])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (~(a = 0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 ((a = 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 ((~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (~$greatereq(a, 0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[24, 19])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 ($greatereq(a, 0) | $greatereq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ($greatereq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 ($greatereq(a, 0) | $lesseq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 ($lesseq($quotient_e(0, a), 0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[17, 29, 27])).
% 0.18/0.37 % SZS output end Proof
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