TSTP Solution File: ARI708_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI708_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ARI708_1 : TPTP v8.1.0. Released v6.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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 01:52:45 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.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(d_type, type, (
% 0.13/0.39 d: $int)).
% 0.13/0.39 tff(c_type, type, (
% 0.13/0.39 c: $int)).
% 0.13/0.39 tff(b_type, type, (
% 0.13/0.39 b: $int)).
% 0.13/0.39 tff(a_type, type, (
% 0.13/0.39 a: $int)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((0 = $sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d)))))) <=> ($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))) = 0)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))) = 0) <=> (0 = $sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))))),
% 0.13/0.39 inference(symmetry,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (($sum($product(c, c), $sum($product(d, d), $product(-2, $product(c, d)))) = b) <=> ($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))) = 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ($sum($product(c, c), $sum($product(-2, $product(c, d)), $product(d, d))) = $sum($product(c, c), $sum($product(d, d), $product(-2, $product(c, d))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (($sum($product(c, c), $sum($product(-2, $product(c, d)), $product(d, d))) = b) <=> ($sum($product(c, c), $sum($product(d, d), $product(-2, $product(c, d)))) = b)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (($sum($product(c, c), $sum($product(-2, $product(c, d)), $product(d, d))) = b) <=> ($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))) = 0)),
% 0.13/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b) <=> ($sum($product(c, c), $sum($product(-2, $product(c, d)), $product(d, d))) = b)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b) <=> ($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (($product($difference(c, d), $difference(c, d)) = b) <=> ($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(10,axiom,($product($difference(c, d), $difference(c, d)) = b), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq2')).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ($product($sum(c, $product(-1, d)), $sum(c, $product(-1, d))) = b),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ($sum($product(c, c), $sum($product(-2, $product(c, d)), $product(d, d))) = b),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))) = 0),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (0 = $sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ((~(0 = $sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))))) | $lesseq($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ($lesseq($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((0 = $sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d)))))) <=> ($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))) = 0)),
% 0.13/0.39 inference(commutativity,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))) = 0) <=> (0 = $sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))))),
% 0.13/0.39 inference(symmetry,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (($sum(a, $sum($product(-2, $product(c, d)), $sum($product(-1, $product(d, d)), $product(-1, $product(c, c))))) = 0) <=> ($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))) = 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (($sum(a, $product(-1, $product($sum(c, d), $sum(d, c)))) = 0) <=> ($sum(a, $sum($product(-2, $product(c, d)), $sum($product(-1, $product(d, d)), $product(-1, $product(c, c))))) = 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (($sum(a, $product(-1, $product($sum(c, d), $sum(d, c)))) = 0) <=> ($sum(a, $product(-1, $product($sum(c, d), $sum(d, c)))) = 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,axiom,($sum(a, $product(-1, $product($sum(c, d), $sum(d, c)))) = 0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','eq1')).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ($sum(a, $product(-1, $product($sum(c, d), $sum(d, c)))) = 0),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ($sum(a, $sum($product(-2, $product(c, d)), $sum($product(-1, $product(d, d)), $product(-1, $product(c, c))))) = 0),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))) = 0),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (0 = $sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~(0 = $sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))))) | $lesseq($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ($lesseq($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~(0 = $sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))))) | $greatereq($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ($greatereq($sum(b, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(2, $product(c, d))))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 15])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 ((~(0 = $sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))))) | $greatereq($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 ($greatereq($sum(a, $sum($product(-1, $product(c, c)), $sum($product(-1, $product(d, d)), $product(-2, $product(c, d))))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 27])).
% 0.13/0.40 tff(34,assumption,(~$greatereq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0)), introduced(assumption)).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[34, 33, 31])).
% 0.13/0.40 tff(36,plain,($greatereq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((0 = $sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d)))))) <=> ($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0) <=> (0 = $sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0)) <=> (~(0 = $sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d)))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0)) <=> (~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~($sum($sum(a, b), $product(-1, $product(2, $sum($product(c, c), $product(d, d))))) = 0)) <=> (~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(42,axiom,(~($sum($sum(a, b), $product(-1, $product(2, $sum($product(c, c), $product(d, d))))) = 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (~($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))) = 0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (~(0 = $sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[44, 39])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((0 = $sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d)))))) | (~$lesseq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0)) | (~$greatereq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~$lesseq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0)) | (~$greatereq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (~$lesseq($sum(a, $sum(b, $sum($product(-2, $product(c, c)), $product(-2, $product(d, d))))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[48, 29, 17])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------