TSTP Solution File: ARI686_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI686_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 17:02:36 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI686_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 : n006.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 01:37:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(a_type, type, (
% 0.13/0.40 a: $int)).
% 0.13/0.40 tff(1,assumption,(~$greatereq(a, 0)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 ((0 = $sum($product(2, a), $product(-5, $product(a, a)))) <=> ($sum($product(2, a), $product(-5, $product(a, a))) = 0)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (($sum($product(2, a), $product(-5, $product(a, a))) = 0) <=> (0 = $sum($product(2, a), $product(-5, $product(a, a))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (($product(5, $product(a, a)) = $product(2, a)) <=> ($sum($product(2, a), $product(-5, $product(a, a))) = 0)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (($product(5, $product(a, a)) = $product(2, a)) <=> ($product(5, $product(a, a)) = $product(2, a))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (($product($product(5, a), a) = $product(2, a)) <=> ($product(5, $product(a, a)) = $product(2, a))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,axiom,($product($product(5, a), a) = $product(2, a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq1')).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ($product(5, $product(a, a)) = $product(2, a)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ($product(5, $product(a, a)) = $product(2, a)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ($sum($product(2, a), $product(-5, $product(a, a))) = 0),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (0 = $sum($product(2, a), $product(-5, $product(a, a)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 ((~(0 = $sum($product(2, a), $product(-5, $product(a, a))))) | $greatereq($sum($product(2, a), $product(-5, $product(a, a))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 ($greatereq($sum($product(2, a), $product(-5, $product(a, a))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.40 tff(14,assumption,(~$lesseq($product(a, a), 0)), introduced(assumption)).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[14, 13, 1])).
% 0.13/0.40 tff(16,plain,($lesseq($product(a, a), 0) | $greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ($lesseq($product(a, a), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[16, 1])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ($greatereq(a, 0) | (~$lesseq($product(a, a), 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[18, 1, 17])).
% 0.13/0.40 tff(20,plain,($greatereq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(21,assumption,(~$greatereq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0)), introduced(assumption)).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((0 = $sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))))))) <=> ($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))) = 0)),
% 0.13/0.41 inference(commutativity,[status(thm)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))) = 0) <=> (0 = $sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))))),
% 0.13/0.41 inference(symmetry,[status(thm)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0) <=> ($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))) = 0)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0) <=> ($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (($product(a, $sum(a, $product(-1, $product($product(2, a), $sum(a, $product($product(3, a), $sum(a, $product(-1, $product($product(4, a), $sum(a, $product($product(5, a), $sum(a, $product(-1, $product($product(6, a), $sum(a, $product($product(7, a), $sum(a, $product(-1, $product($product(8, a), $sum(9, a)))))))))))))))))))) = 0) <=> ($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(27,axiom,($product(a, $sum(a, $product(-1, $product($product(2, a), $sum(a, $product($product(3, a), $sum(a, $product(-1, $product($product(4, a), $sum(a, $product($product(5, a), $sum(a, $product(-1, $product($product(6, a), $sum(a, $product($product(7, a), $sum(a, $product(-1, $product($product(8, a), $sum(9, a)))))))))))))))))))) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq2')).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 ($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ($product(a, $sum(a, $product(-2, $product(a, $sum(a, $product(3, $product(a, $sum(a, $product(-4, $product(a, $sum(a, $product(5, $product(a, $sum(a, $product(-6, $product(a, $sum(a, $product(7, $product(a, $sum(a, $product(-8, $product(a, $sum(9, a))))))))))))))))))))))) = 0),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))) = 0),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (0 = $sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 ((~(0 = $sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))))) | $greatereq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ($greatereq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((~(0 = $sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))))) | $lesseq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 ($lesseq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 ((~(0 = $sum($product(2, a), $product(-5, $product(a, a))))) | $lesseq($sum($product(2, a), $product(-5, $product(a, a))), 0)),
% 0.13/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ($lesseq($sum($product(2, a), $product(-5, $product(a, a))), 0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[36, 11])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 ((~$lesseq($sum($product(2, a), $product(-5, $product(a, a))), 0)) | (~$greatereq($sum($product(2, a), $product(-5, $product(a, a))), 0)) | $greatereq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0) | (~$lesseq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0)) | (~$greatereq(a, 0)) | (~$greatereq($sum($product(a, a), $sum($product(-2, $product(a, $product(a, a))), $sum($product(-6, $product(a, $product(a, $product(a, a)))), $sum($product(24, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(120, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-720, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $sum($product(357840, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $product(40320, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))), 0))),
% 0.13/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[38, 37, 13, 35, 33, 21, 20])).
% 0.13/0.42 tff(40,plain,($greatereq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(41,plain,
% 0.13/0.42 ((0 = $sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))))) <=> ($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))) = 0)),
% 0.13/0.42 inference(commutativity,[status(thm)],[])).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 (($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))) = 0) <=> (0 = $sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))),
% 0.13/0.42 inference(symmetry,[status(thm)],[41])).
% 0.13/0.42 tff(43,plain,
% 0.13/0.42 ((~($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))) = 0)) <=> (~(0 = $sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0)) <=> (~($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))) = 0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0)) <=> (~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 ((~($sum($product(2, $product($product($product($product($product($product($product(a, a), a), a), a), a), a), a)), $product(-1, $sum($sum($sum($sum($sum($product(612, a), $product(-1, $product(a, a))), $product(-2, $product($product(a, a), a))), $product(2, $product($product($product($product(a, a), a), a), a))), $product(-2, $product($product($product($product($product(a, a), a), a), a), a))), $product(-2, $product($product($product($product($product($product(a, a), a), a), a), a), a))))) = 0)) <=> (~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,axiom,(~($sum($product(2, $product($product($product($product($product($product($product(a, a), a), a), a), a), a), a)), $product(-1, $sum($sum($sum($sum($sum($product(612, a), $product(-1, $product(a, a))), $product(-2, $product($product(a, a), a))), $product(2, $product($product($product($product(a, a), a), a), a))), $product(-2, $product($product($product($product($product(a, a), a), a), a), a))), $product(-2, $product($product($product($product($product($product(a, a), a), a), a), a), a))))) = 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 (~($sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))), $sum($product(-612, a), $sum($product(a, a), $sum($product(2, $product(a, $product(a, a))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $product(2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))) = 0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 (~($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))) = 0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (~(0 = $sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ((0 = $sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))))))))))) | (~$lesseq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0)) | (~$greatereq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((~$lesseq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0)) | (~$greatereq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (~$lesseq($sum($product(612, a), $sum($product(-1, $product(a, a)), $sum($product(-2, $product(a, $product(a, a))), $sum($product(2, $product(a, $product(a, $product(a, $product(a, a))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), $sum($product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), $product(-2, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))))))))))), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[53, 40])).
% 0.19/0.43 tff(55,assumption,(~$lesseq(a, 0)), introduced(assumption)).
% 0.19/0.43 tff(56,assumption,($greatereq($sum($product(a, a), $product(-1, a)), 0)), introduced(assumption)).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[55, 13, 56])).
% 0.19/0.43 tff(58,plain,((~$greatereq($sum($product(a, a), $product(-1, a)), 0)) | $lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (~$greatereq($sum($product(a, a), $product(-1, a)), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 ((~$lesseq($sum($product(2, a), $product(-5, $product(a, a))), 0)) | $greatereq($sum($product(a, a), $product(-1, a)), 0) | (~$lesseq($product(a, a), 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (~$lesseq($product(a, a), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[60, 59, 37])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 ($greatereq($product(a, a), 0) | $lesseq($product(a, a), 0)),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 ($greatereq($product(a, a), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 ((~$greatereq($product(a, a), 0)) | $greatereq($sum($product(a, a), $product(-1, a)), 0) | $lesseq(a, 0)),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[64, 55, 59, 63])).
% 0.19/0.43 tff(66,plain,($lesseq(a, 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a)))))), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 66, 20])).
% 0.19/0.43 tff(69,assumption,($lesseq($product(a, $product(a, $product(a, $product(a, a)))), 0)), introduced(assumption)).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, a))))), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, a))))), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[70, 66, 20])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, a)), 0) | (~$lesseq(a, 0)) | (~$greatereq(a, 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, a)), 0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 66, 20])).
% 0.19/0.43 tff(74,assumption,(~$greatereq($product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), 0)), introduced(assumption)).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 ($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), 0)),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.43 tff(77,plain,($greatereq($product(a, $product(a, $product(a, $product(a, $product(a, $product(a, $product(a, a))))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[77, 66, 73, 37, 71, 69, 68, 54])).
% 0.19/0.43 tff(79,plain,(~$lesseq($product(a, $product(a, $product(a, $product(a, a)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ($lesseq($product(a, $product(a, $product(a, $product(a, a)))), 0) | (~$lesseq(a, 0))),
% 0.19/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 66, 79])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------