TSTP Solution File: ARI711_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI711_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 17:02:42 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI711_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n004.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 01:48:05 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.
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(b_type, type, (
% 0.20/0.50 b: $int)).
% 0.20/0.50 tff(a_type, type, (
% 0.20/0.50 a: $int)).
% 0.20/0.50 tff(c_type, type, (
% 0.20/0.50 c: $int)).
% 0.20/0.50 tff(1,assumption,(~$lesseq($sum(1, $sum(c, $sum(a, b))), 0)), introduced(assumption)).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 ((0 = $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c))))))) <=> ($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0)),
% 0.20/0.50 inference(commutativity,[status(thm)],[])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0) <=> (0 = $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[2])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0) <=> ($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (($product($product($product($sum($sum($sum(a, b), c), 1), $sum($sum($sum(a, b), c), 1)), $sum($sum($sum(a, b), c), 1)), $sum($sum($sum(a, b), c), 1)) = 0) <=> ($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(6,axiom,($product($product($product($sum($sum($sum(a, b), c), 1), $sum($sum($sum(a, b), c), 1)), $sum($sum($sum(a, b), c), 1)), $sum($sum($sum(a, b), c), 1)) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq')).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 ($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 ($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))) = 0),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (0 = $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 ((~(0 = $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))))) | $lesseq($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 ($lesseq($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 ($lesseq($sum(1, $sum(c, $sum(a, b))), 0) | (~$lesseq($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))), 0))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.20/0.50 tff(14,plain,($lesseq($sum(1, $sum(c, $sum(a, b))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(15,assumption,(~$greatereq($sum(1, $sum(c, $sum(a, b))), 0)), introduced(assumption)).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 ($greatereq($sum(1, $sum(c, $sum(a, b))), 0) | (~$lesseq($product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $product($sum(1, $sum(a, $sum(b, c))), $sum(1, $sum(a, $sum(b, c)))))), 0))),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[16, 11, 15])).
% 0.20/0.50 tff(18,plain,($greatereq($sum(1, $sum(c, $sum(a, b))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(19,assumption,($greatereq($sum(1, $sum(c, $sum(a, b))), 0)), introduced(assumption)).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 ($lesseq($sum(1, $sum(c, $sum(a, b))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.50 tff(21,assumption,(~$greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)), introduced(assumption)).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 ((~$greatereq($sum(1, $sum(c, $sum(a, b))), 0)) | (~$lesseq($sum(1, $sum(c, $sum(a, b))), 0)) | $greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[22, 21, 20, 19])).
% 0.20/0.50 tff(24,plain,((~$greatereq($sum(1, $sum(c, $sum(a, b))), 0)) | $greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 ($greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 ((-1 = $sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c)))))))))))))))))))))))))))))))))))))) <=> ($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)),
% 0.20/0.51 inference(commutativity,[status(thm)],[])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1) <=> (-1 = $sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))))),
% 0.20/0.51 inference(symmetry,[status(thm)],[26])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 ((~($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)) <=> (~(-1 = $sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c)))))))))))))))))))))))))))))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[27])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 ((~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)) <=> (~($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 ((~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)) <=> (~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 ((~($sum($product($product($product(c, c), c), c), $product(-1, $sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference($product(-1, 1), $product(4, a)), $product(-6, $product(a, a))), $product(-4, $product($product(a, a), a))), $product(-1, $product($product($product(a, a), a), a))), $product(4, b)), $product(-12, $product(b, a))), $product(-6, $product(b, b))), $product(-12, $product($product(b, a), a))), $product(-12, $product($product(b, b), a))), $product(-4, $product($product(b, b), b))), $product(-4, $product($product($product(b, a), a), a))), $product(-6, $product($product($product(b, b), a), a))), $product(-4, $product($product($product(b, b), b), a))), $product(-1, $product($product($product(b, b), b), b))), $product(4, c)), $product(-12, $product(c, a))), $product(-12, $product(c, b))), $product(-6, $product(c, c))), $product(-12, $product($product(c, a), a))), $product(-24, $product($product(c, b), a))), $product(-12, $product($product(c, b), b))), $product(-12, $product($product(c, c), a))), $product(-12, $product($product(c, c), b))), $product(-4, $product($product(c, c), c))), $product(-4, $product($product($product(c, a), a), a))), $product(-12, $product($product($product(c, b), a), a))), $product(-12, $product($product($product(c, b), b), a))), $product(-4, $product($product($product(c, b), b), b))), $product(-6, $product($product($product(c, c), a), a))), $product(-12, $product($product($product(c, c), b), a))), $product(-6, $product($product($product(c, c), b), b))), $product(-4, $product($product($product(c, c), c), a))), $product(-4, $product($product($product(c, c), c), b))))) = 0)) <=> (~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(32,axiom,(~($sum($product($product($product(c, c), c), c), $product(-1, $sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference($product(-1, 1), $product(4, a)), $product(-6, $product(a, a))), $product(-4, $product($product(a, a), a))), $product(-1, $product($product($product(a, a), a), a))), $product(4, b)), $product(-12, $product(b, a))), $product(-6, $product(b, b))), $product(-12, $product($product(b, a), a))), $product(-12, $product($product(b, b), a))), $product(-4, $product($product(b, b), b))), $product(-4, $product($product($product(b, a), a), a))), $product(-6, $product($product($product(b, b), a), a))), $product(-4, $product($product($product(b, b), b), a))), $product(-1, $product($product($product(b, b), b), b))), $product(4, c)), $product(-12, $product(c, a))), $product(-12, $product(c, b))), $product(-6, $product(c, c))), $product(-12, $product($product(c, a), a))), $product(-24, $product($product(c, b), a))), $product(-12, $product($product(c, b), b))), $product(-12, $product($product(c, c), a))), $product(-12, $product($product(c, c), b))), $product(-4, $product($product(c, c), c))), $product(-4, $product($product($product(c, a), a), a))), $product(-12, $product($product($product(c, b), a), a))), $product(-12, $product($product($product(c, b), b), a))), $product(-4, $product($product($product(c, b), b), b))), $product(-6, $product($product($product(c, c), a), a))), $product(-12, $product($product($product(c, c), b), a))), $product(-6, $product($product($product(c, c), b), b))), $product(-4, $product($product($product(c, c), c), a))), $product(-4, $product($product($product(c, c), c), b))))) = 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 (~($sum($product(c, $product(c, $product(c, c))), $sum($product(4, a), $sum($product(6, $product(a, a)), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(4, b), $sum($product(12, $product(a, b)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(4, c), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(6, $product(c, c)), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 (~($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))) = -1)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 (~(-1 = $sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 ((-1 = $sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c)))))))))))))))))))))))))))))))))))))) | (~$lesseq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)) | (~$greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 ((~$lesseq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)) | (~$greatereq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (~$lesseq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[38, 25])).
% 0.20/0.53 tff(40,plain,
% 0.20/0.53 ((~$greatereq($sum(1, $sum(c, $sum(a, b))), 0)) | $lesseq($sum($product(4, a), $sum($product(4, b), $sum($product(4, c), $sum($product(6, $product(c, c)), $sum($product(6, $product(a, a)), $sum($product(6, $product(b, b)), $sum($product(12, $product(a, b)), $sum($product(12, $product(a, c)), $sum($product(12, $product(b, c)), $sum($product(4, $product(c, $product(c, c))), $sum($product(c, $product(c, $product(c, c))), $sum($product(4, $product(a, $product(a, a))), $sum($product(a, $product(a, $product(a, a))), $sum($product(12, $product(a, $product(a, b))), $sum($product(12, $product(a, $product(b, b))), $sum($product(4, $product(b, $product(b, b))), $sum($product(4, $product(a, $product(a, $product(a, b)))), $sum($product(6, $product(a, $product(a, $product(b, b)))), $sum($product(4, $product(a, $product(b, $product(b, b)))), $sum($product(b, $product(b, $product(b, b))), $sum($product(12, $product(a, $product(a, c))), $sum($product(24, $product(a, $product(b, c))), $sum($product(12, $product(b, $product(b, c))), $sum($product(12, $product(a, $product(c, c))), $sum($product(12, $product(b, $product(c, c))), $sum($product(4, $product(a, $product(a, $product(a, c)))), $sum($product(12, $product(a, $product(a, $product(b, c)))), $sum($product(12, $product(a, $product(b, $product(b, c)))), $sum($product(4, $product(b, $product(b, $product(b, c)))), $sum($product(6, $product(a, $product(a, $product(c, c)))), $sum($product(12, $product(a, $product(b, $product(c, c)))), $sum($product(6, $product(b, $product(b, $product(c, c)))), $sum($product(4, $product(a, $product(c, $product(c, c)))), $product(4, $product(b, $product(c, $product(c, c))))))))))))))))))))))))))))))))))))), -1) | (~$lesseq($sum(1, $sum(c, $sum(a, b))), 0))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[40, 39, 18, 14])).
% 0.20/0.53 % SZS output end Proof
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