TSTP Solution File: ARI698_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI698_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 17:02:38 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ARI698_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.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 01:59:20 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 tff(x1_type, type, (
% 0.21/0.46 x1: $int)).
% 0.21/0.46 tff(x2_type, type, (
% 0.21/0.46 x2: $int)).
% 0.21/0.46 tff(x3_type, type, (
% 0.21/0.46 x3: $int)).
% 0.21/0.46 tff(x4_type, type, (
% 0.21/0.46 x4: $int)).
% 0.21/0.46 tff(x5_type, type, (
% 0.21/0.46 x5: $int)).
% 0.21/0.46 tff(x6_type, type, (
% 0.21/0.46 x6: $int)).
% 0.21/0.46 tff(n_type, type, (
% 0.21/0.46 n: $int)).
% 0.21/0.46 tff(1,plain,
% 0.21/0.46 (($lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0) & $greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) <=> (~((~$lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(2,plain,
% 0.21/0.46 (($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0) & $greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(3,plain,
% 0.21/0.46 (($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> (~((~$lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[2, 1])).
% 0.21/0.46 tff(4,plain,
% 0.21/0.46 (($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(5,plain,
% 0.21/0.46 (($sum($product(n, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(6,plain,
% 0.21/0.46 (($difference($difference($difference($difference($sum($product(n, x6), $product(1, x5)), x4), x3), x2), x1) = 0) <=> ($sum($product(n, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(7,axiom,($difference($difference($difference($difference($sum($product(n, x6), $product(1, x5)), x4), x3), x2), x1) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq4')).
% 0.21/0.46 tff(8,plain,
% 0.21/0.46 ($sum($product(n, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.46 tff(9,plain,
% 0.21/0.46 ($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.21/0.46 tff(10,plain,
% 0.21/0.46 ($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.46 tff(11,plain,
% 0.21/0.46 (~((~$lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.46 tff(12,plain,
% 0.21/0.46 ($lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)),
% 0.21/0.47 inference(or_elim,[status(thm)],[11])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (($lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(14,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0) <=> ($lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[14, 13])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (($sum($product(n, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (($sum($sum($sum($difference($sum($product(n, x6), $product(0, x5)), x4), $product(1, x3)), $product(1, x2)), $product(1, x1)) = 0) <=> ($sum($product(n, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(19,axiom,($sum($sum($sum($difference($sum($product(n, x6), $product(0, x5)), x4), $product(1, x3)), $product(1, x2)), $product(1, x1)) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq6')).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 ($sum($product(n, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 ($greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)),
% 0.21/0.47 inference(or_elim,[status(thm)],[23])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (($lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0) & $greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) <=> (~((~$lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0) <=> ($lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0) & $greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0) <=> (~((~$lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[26, 25])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0) <=> ($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (($sum($product(n, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0) <=> ($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (($difference($difference($sum($sum($sum($product(n, x6), $product(0, x5)), $product(0, x4)), $product(1, x3)), x2), x1) = 0) <=> ($sum($product(n, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(31,axiom,($difference($difference($sum($sum($sum($product(n, x6), $product(0, x5)), $product(0, x4)), $product(1, x3)), x2), x1) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq8')).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 ($sum($product(n, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (~((~$lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 ($lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)),
% 0.21/0.47 inference(or_elim,[status(thm)],[35])).
% 0.21/0.47 tff(37,assumption,(~$greatereq(x1, 0)), introduced(assumption)).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (($lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0) <=> ($lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[39, 38])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (($sum($product(n, x6), $sum($product(-1, x2), x1)) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (($sum($difference($sum($sum($sum($product(n, x6), $product(0, x5)), $product(0, x4)), $product(0, x3)), x2), $product(1, x1)) = 0) <=> ($sum($product(n, x6), $sum($product(-1, x2), x1)) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(44,axiom,($sum($difference($sum($sum($sum($product(n, x6), $product(0, x5)), $product(0, x4)), $product(0, x3)), x2), $product(1, x1)) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq10')).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 ($sum($product(n, x6), $sum($product(-1, x2), x1)) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x2), x1)) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 ($greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)),
% 0.21/0.47 inference(or_elim,[status(thm)],[48])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (($lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0) & $greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[51, 50])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (($sum($product(n, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0) <=> ($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (($difference($difference($difference($difference($difference($product(n, x6), x5), x4), x3), x2), x1) = 0) <=> ($sum($product(n, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(56,axiom,($difference($difference($difference($difference($difference($product(n, x6), x5), x4), x3), x2), x1) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq3')).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 ($sum($product(n, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.47 tff(58,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))) = 0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[58, 53])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (~((~$lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 ($lesseq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[60])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (($lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0) & $greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) <=> (~((~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0) <=> ($lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0) & $greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0) <=> (~((~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[63, 62])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0) <=> ($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (($sum(x6, $sum($product(n, x5), $sum($product(n, x4), $sum($product(n, x3), $sum($product(n, x2), $product(n, x1)))))) = 0) <=> ($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (($sum($sum($sum($sum($sum($product(1, x6), $product(n, x5)), $product(n, x4)), $product(n, x3)), $product(n, x2)), $product(n, x1)) = 0) <=> ($sum(x6, $sum($product(n, x5), $sum($product(n, x4), $sum($product(n, x3), $sum($product(n, x2), $product(n, x1)))))) = 0)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(68,axiom,($sum($sum($sum($sum($sum($product(1, x6), $product(n, x5)), $product(n, x4)), $product(n, x3)), $product(n, x2)), $product(n, x1)) = 0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq2')).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 ($sum(x6, $sum($product(n, x5), $sum($product(n, x4), $sum($product(n, x3), $sum($product(n, x2), $product(n, x1)))))) = 0),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 ($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 ($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))) = 0),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 (~((~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 ($lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[72])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[73, 61, 49, 37, 36, 24, 12])).
% 0.21/0.48 tff(75,plain,($greatereq(x1, 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ($greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[72])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 ($lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[48])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 ($greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[35])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 ($lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[23])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 ($greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[11])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 ($greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)),
% 0.21/0.48 inference(or_elim,[status(thm)],[60])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ((~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x5), $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | $lesseq(x1, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 ($lesseq(x1, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[82, 81, 80, 79, 78, 77, 76])).
% 0.21/0.48 tff(84,assumption,(~$greatereq(x2, 0)), introduced(assumption)).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[76, 81, 77, 12, 36, 24, 84])).
% 0.21/0.48 tff(86,plain,($greatereq(x2, 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 ((~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq(x1, 0)) | (~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | $lesseq(x2, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 ($lesseq(x2, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[87, 80, 79, 78, 77, 73, 75])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 ((~$greatereq(x1, 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | $greatereq(x3, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 ($greatereq(x3, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[89, 77, 78, 75])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 ((~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$lesseq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq(x2, 0)) | (~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | $lesseq(x3, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 ($lesseq(x3, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[91, 80, 79, 36, 49, 73, 86])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 ((~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq(x2, 0)) | $greatereq(x4, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 ($greatereq(x4, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[93, 12, 79, 78, 49, 76, 86])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 ((~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq(x1, 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | $lesseq(x4, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ($lesseq(x4, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[95, 80, 24, 78, 77, 73, 75])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 ((~$greatereq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq(x1, 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | $greatereq(x5, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 ($greatereq(x5, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[97, 80, 79, 78, 77, 76, 75])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 ((~$lesseq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$greatereq(x1, 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | $lesseq(x6, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 ($lesseq(x6, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[99, 80, 79, 78, 77, 73, 75])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 ((~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$lesseq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$greatereq(x2, 0)) | $lesseq(x5, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 ($lesseq(x5, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[101, 12, 79, 78, 49, 73, 86])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 ((~$greatereq($sum($product(1000, x6), $sum($product(-1, x2), x1)), 0)) | (~$lesseq($sum(x6, $sum($product(1000, x5), $sum($product(1000, x4), $sum($product(1000, x3), $sum($product(1000, x2), $product(1000, x1)))))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x3, $sum($product(-1, x2), $product(-1, x1)))), 0)) | (~$lesseq($sum($product(1000, x6), $sum($product(-1, x4), $sum(x3, $sum(x2, x1)))), 0)) | (~$greatereq($sum($product(1000, x6), $sum(x5, $sum($product(-1, x4), $sum($product(-1, x3), $sum($product(-1, x2), $product(-1, x1)))))), 0)) | (~$greatereq(x2, 0)) | $greatereq(x6, 0)),
% 0.21/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 ($greatereq(x6, 0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[103, 80, 79, 78, 49, 73, 86])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 ((~(~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))) <=> ((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (((~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)))) & (~((~$lesseq(x5, 0)) | (~$greatereq(x5, 0)))) & (~((~$lesseq(x4, 0)) | (~$greatereq(x4, 0)))) & (~((~$lesseq(x3, 0)) | (~$greatereq(x3, 0)))) & (~((~$lesseq(x2, 0)) | (~$greatereq(x2, 0)))) & (~((~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))) <=> (~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (($lesseq(x1, 0) & $greatereq(x1, 0)) <=> (~((~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 ((x1 = 0) <=> ($lesseq(x1, 0) & $greatereq(x1, 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ((x1 = 0) <=> (~((~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[108, 107])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (($lesseq(x2, 0) & $greatereq(x2, 0)) <=> (~((~$lesseq(x2, 0)) | (~$greatereq(x2, 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 ((x2 = 0) <=> ($lesseq(x2, 0) & $greatereq(x2, 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 ((x2 = 0) <=> (~((~$lesseq(x2, 0)) | (~$greatereq(x2, 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[111, 110])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (($lesseq(x3, 0) & $greatereq(x3, 0)) <=> (~((~$lesseq(x3, 0)) | (~$greatereq(x3, 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 ((x3 = 0) <=> ($lesseq(x3, 0) & $greatereq(x3, 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 ((x3 = 0) <=> (~((~$lesseq(x3, 0)) | (~$greatereq(x3, 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[114, 113])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (($lesseq(x4, 0) & $greatereq(x4, 0)) <=> (~((~$lesseq(x4, 0)) | (~$greatereq(x4, 0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 ((x4 = 0) <=> ($lesseq(x4, 0) & $greatereq(x4, 0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 ((x4 = 0) <=> (~((~$lesseq(x4, 0)) | (~$greatereq(x4, 0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[117, 116])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (($lesseq(x5, 0) & $greatereq(x5, 0)) <=> (~((~$lesseq(x5, 0)) | (~$greatereq(x5, 0))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 ((x5 = 0) <=> ($lesseq(x5, 0) & $greatereq(x5, 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 ((x5 = 0) <=> (~((~$lesseq(x5, 0)) | (~$greatereq(x5, 0))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[120, 119])).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 (($lesseq(x6, 0) & $greatereq(x6, 0)) <=> (~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 ((x6 = 0) <=> ($lesseq(x6, 0) & $greatereq(x6, 0))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 ((x6 = 0) <=> (~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[123, 122])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 (((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0)) <=> ((~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)))) & (~((~$lesseq(x5, 0)) | (~$greatereq(x5, 0)))) & (~((~$lesseq(x4, 0)) | (~$greatereq(x4, 0)))) & (~((~$lesseq(x3, 0)) | (~$greatereq(x3, 0)))) & (~((~$lesseq(x2, 0)) | (~$greatereq(x2, 0)))) & (~((~$lesseq(x1, 0)) | (~$greatereq(x1, 0)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[124, 121, 118, 115, 112, 109])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 (((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0)) <=> (~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[125, 106])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 ((~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0))) <=> (~(~((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.49 tff(128,plain,
% 0.21/0.49 ((~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0))) <=> ((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[127, 105])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 ((~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0))) <=> (~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 ((~((((((x6 = 0) & (x5 = 0)) & (x4 = 0)) & (x3 = 0)) & (x2 = 0)) & (x1 = 0))) <=> (~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(131,axiom,(~((((((x6 = 0) & (x5 = 0)) & (x4 = 0)) & (x3 = 0)) & (x2 = 0)) & (x1 = 0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 (~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 (~((x6 = 0) & (x5 = 0) & (x4 = 0) & (x3 = 0) & (x2 = 0) & (x1 = 0))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[132, 129])).
% 0.21/0.49 tff(134,plain,
% 0.21/0.49 ((~$lesseq(x6, 0)) | (~$greatereq(x6, 0)) | (~$lesseq(x5, 0)) | (~$greatereq(x5, 0)) | (~$lesseq(x4, 0)) | (~$greatereq(x4, 0)) | (~$lesseq(x3, 0)) | (~$greatereq(x3, 0)) | (~$lesseq(x2, 0)) | (~$greatereq(x2, 0)) | (~$lesseq(x1, 0)) | (~$greatereq(x1, 0))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[133, 128])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[134, 104, 102, 100, 98, 96, 94, 92, 90, 88, 86, 83, 75])).
% 0.21/0.49 % SZS output end Proof
%------------------------------------------------------------------------------