TSTP Solution File: ARI681_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI681_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 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ARI681_1 : TPTP v8.1.0. Released v6.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 01:41:50 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(c_type, type, (
% 0.13/0.39 c: $int)).
% 0.13/0.39 tff(d_type, type, (
% 0.13/0.39 d: $int)).
% 0.13/0.39 tff(b_type, type, (
% 0.13/0.39 b: $int)).
% 0.13/0.39 tff(1,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(~$lesseq(c, 0)), introduced(assumption)).
% 0.13/0.39 tff(3,assumption,($lesseq(a, 0)), introduced(assumption)).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~$lesseq($product(a, c), 0)) <=> (~$lesseq($product(a, c), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ($less(0, $product(a, c)) <=> (~$lesseq($product(a, c), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,($less(0, $product(a, c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~$lesseq($product(a, c), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~$lesseq($product(a, c), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((~$lesseq(a, 0)) | $lesseq($product(a, c), 0) | $lesseq(c, 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[9, 8, 2, 3])).
% 0.13/0.39 tff(11,plain,((~$lesseq(a, 0)) | $lesseq(c, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~$lesseq(a, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[11, 2])).
% 0.13/0.39 tff(13,assumption,(~$greatereq(b, 0)), introduced(assumption)).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~$lesseq($product(a, b), 0)) <=> (~$lesseq($product(a, b), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 ($less(0, $product(a, b)) <=> (~$lesseq($product(a, b), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(16,axiom,($less(0, $product(a, b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_002')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~$lesseq($product(a, b), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (~$lesseq($product(a, b), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ($greatereq(b, 0) | $lesseq($product(a, b), 0) | $lesseq(a, 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[19, 18, 13, 1])).
% 0.13/0.39 tff(21,plain,($greatereq(b, 0) | $lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ($greatereq(b, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 12])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((0 = b) <=> (b = 0)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((b = 0) <=> (0 = b)),
% 0.13/0.39 inference(symmetry,[status(thm)],[23])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~(b = 0)) <=> (~(0 = b))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~(b = 0)) | $lesseq($product(a, b), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~(b = 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 18])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~(0 = b)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((0 = b) | (~$lesseq(b, 0)) | (~$greatereq(b, 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ((~$lesseq(b, 0)) | (~$greatereq(b, 0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~$lesseq(b, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[30, 22])).
% 0.13/0.39 tff(32,assumption,(~$lesseq(d, 0)), introduced(assumption)).
% 0.13/0.39 tff(33,assumption,(~$lesseq(b, 0)), introduced(assumption)).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ($lesseq($product(b, d), 0) <=> $lesseq($product(d, b), 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ($lesseq($product(b, d), 0) <=> $lesseq($product(b, d), 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~(~$lesseq($product(b, d), 0))) <=> $lesseq($product(b, d), 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ($less(0, $product(b, d)) <=> (~$lesseq($product(b, d), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~$less(0, $product(b, d))) <=> (~(~$lesseq($product(b, d), 0)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~$less(0, $product(b, d))) <=> $lesseq($product(b, d), 0)),
% 0.13/0.39 inference(transitivity,[status(thm)],[38, 36])).
% 0.13/0.39 tff(40,axiom,(~$less(0, $product(b, d))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_003')).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ($lesseq($product(b, d), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ($lesseq($product(b, d), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ($lesseq($product(d, b), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ($lesseq(b, 0) | $lesseq(d, 0) | (~$lesseq($product(d, b), 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[44, 43, 33, 32])).
% 0.13/0.39 tff(46,plain,($lesseq(d, 0) | $lesseq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ($lesseq(d, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[46, 31])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((0 = d) <=> (d = 0)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ((d = 0) <=> (0 = d)),
% 0.13/0.39 inference(symmetry,[status(thm)],[48])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ((~(d = 0)) <=> (~(0 = d))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~$lesseq($product(c, d), 0)) <=> (~$lesseq($product(c, d), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ($less(0, $product(c, d)) <=> (~$lesseq($product(c, d), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(53,axiom,($less(0, $product(c, d))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_001')).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (~$lesseq($product(c, d), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~$lesseq($product(c, d), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~(d = 0)) | $lesseq($product(c, d), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (~(d = 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (~(0 = d)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((0 = d) | (~$lesseq(d, 0)) | (~$greatereq(d, 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ((~$lesseq(d, 0)) | (~$greatereq(d, 0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (~$greatereq(d, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[60, 47])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ($lesseq(c, 0) | $lesseq($product(c, d), 0) | $greatereq(d, 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[62, 55, 61, 2])).
% 0.13/0.39 tff(64,plain,($lesseq(c, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 ((0 = c) <=> (c = 0)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 ((c = 0) <=> (0 = c)),
% 0.13/0.39 inference(symmetry,[status(thm)],[65])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 ((~(c = 0)) <=> (~(0 = c))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[66])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 ((~(c = 0)) | $lesseq($product(a, c), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (~(c = 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[68, 8])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (~(0 = c)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[69, 67])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ((0 = c) | (~$lesseq(c, 0)) | (~$greatereq(c, 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ((~$lesseq(c, 0)) | (~$greatereq(c, 0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (~$greatereq(c, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[72, 64])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 ($lesseq($product(a, c), 0) | $greatereq(c, 0) | $lesseq(a, 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[74, 8, 73, 1])).
% 0.13/0.39 tff(76,plain,($lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 ($lesseq($product(c, d), 0) | $greatereq(c, 0) | $lesseq(d, 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[77, 55, 32, 73])).
% 0.13/0.39 tff(79,plain,($lesseq(d, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (~$greatereq(d, 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[60, 79])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.40 ($greatereq(b, 0) | (~$lesseq($product(d, b), 0)) | $greatereq(d, 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(82,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[81, 43, 13, 80])).
% 0.13/0.40 tff(83,plain,($greatereq(b, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (~$lesseq(b, 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 83])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 ($lesseq(b, 0) | (~$lesseq(a, 0)) | $lesseq($product(a, b), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[85, 18, 84, 76])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------