TSTP Solution File: ARI707_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI707_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 17:02:41 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI707_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 02:12:00 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(c_type, type, (
% 0.20/0.40 c: $int)).
% 0.20/0.40 tff(d_type, type, (
% 0.20/0.40 d: $int)).
% 0.20/0.40 tff(1,assumption,(~$greatereq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((0 = $sum($product(d, d), $product(-1, c))) <=> ($sum($product(d, d), $product(-1, c)) = 0)),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (($sum($product(d, d), $product(-1, c)) = 0) <=> (0 = $sum($product(d, d), $product(-1, c)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (($sum($product(-1, $product(d, d)), c) = 0) <=> ($sum($product(d, d), $product(-1, c)) = 0)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (($sum($product(-1, $product(d, d)), c) = 0) <=> ($sum($product(-1, $product(d, d)), c) = 0)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (($sum($product(d, d), c) = $product(2, $product(d, d))) <=> ($sum($product(-1, $product(d, d)), c) = 0)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ($product($product(2, d), d) = $product(2, $product(d, d))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (($sum($product(d, d), c) = $product($product(2, d), d)) <=> ($sum($product(d, d), c) = $product(2, $product(d, d)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (($sum($product(d, d), c) = $product($product(2, d), d)) <=> ($sum($product(-1, $product(d, d)), c) = 0)),
% 0.20/0.40 inference(transitivity,[status(thm)],[8, 6])).
% 0.20/0.40 tff(10,axiom,($sum($product(d, d), c) = $product($product(2, d), d)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq')).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 ($sum($product(-1, $product(d, d)), c) = 0),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ($sum($product(-1, $product(d, d)), c) = 0),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ($sum($product(d, d), $product(-1, c)) = 0),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (0 = $sum($product(d, d), $product(-1, c))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 ((~(0 = $sum($product(d, d), $product(-1, c)))) | $greatereq($sum($product(d, d), $product(-1, c)), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 ($greatereq($sum($product(d, d), $product(-1, c)), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~(0 = $sum($product(d, d), $product(-1, c)))) | $lesseq($sum($product(d, d), $product(-1, c)), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 ($lesseq($sum($product(d, d), $product(-1, c)), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 ((~$lesseq($sum($product(d, d), $product(-1, c)), 0)) | (~$greatereq($sum($product(d, d), $product(-1, c)), 0)) | $greatereq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[19, 18, 16, 1])).
% 0.20/0.40 tff(21,plain,($greatereq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 ((0 = $sum($product(c, c), $product(-1, $product(d, $product(d, c))))) <=> ($sum($product(c, c), $product(-1, $product(d, $product(d, c)))) = 0)),
% 0.20/0.40 inference(commutativity,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (($sum($product(c, c), $product(-1, $product(d, $product(d, c)))) = 0) <=> (0 = $sum($product(c, c), $product(-1, $product(d, $product(d, c)))))),
% 0.20/0.40 inference(symmetry,[status(thm)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~($sum($product(c, c), $product(-1, $product(d, $product(d, c)))) = 0)) <=> (~(0 = $sum($product(c, c), $product(-1, $product(d, $product(d, c))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~($product(c, $product(d, d)) = $product(c, c))) <=> (~($sum($product(c, c), $product(-1, $product(d, $product(d, c)))) = 0))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~($product(c, $product(d, d)) = $product(c, c))) <=> (~($product(c, $product(d, d)) = $product(c, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~($product($product(c, d), d) = $product(c, c))) <=> (~($product(c, $product(d, d)) = $product(c, c)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(~($product($product(c, d), d) = $product(c, c))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~($product(c, $product(d, d)) = $product(c, c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~($product(c, $product(d, d)) = $product(c, c))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (~($sum($product(c, c), $product(-1, $product(d, $product(d, c)))) = 0)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~(0 = $sum($product(c, c), $product(-1, $product(d, $product(d, c)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((0 = $sum($product(c, c), $product(-1, $product(d, $product(d, c))))) | (~$lesseq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)) | (~$greatereq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0))),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~$lesseq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)) | (~$greatereq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~$lesseq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[34, 21])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 ((~$lesseq($sum($product(d, d), $product(-1, c)), 0)) | (~$greatereq($sum($product(d, d), $product(-1, c)), 0)) | $lesseq($sum($product(c, c), $product(-1, $product(d, $product(d, c)))), 0)),
% 0.20/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[36, 18, 16, 35])).
% 0.20/0.41 % SZS output end Proof
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