TSTP Solution File: SYO523_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO523_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Fri Sep 30 01:40:48 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO523_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 13:53:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: $int > $int)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~$lesseq(9, f(3))) <=> (~$greatereq(f(3), 9))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~$lesseq(9, f(3))) <=> (~$lesseq(9, f(3)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~(((((![X: $int, Y: $int] : ((f(X) = f(Y)) => (X = Y)) & $less(6, f(3))) & $less(f(3), 9)) & $less(6, f(4))) & $less(f(4), 9)) => ($lesseq(f(5), 6) | $lesseq(9, f(5))))) <=> (~($lesseq(f(5), 6) | $lesseq(9, f(5)) | (~(![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y)) & (~$lesseq(f(3), 6)) & (~$lesseq(9, f(3))) & (~$lesseq(f(4), 6)) & (~$lesseq(9, f(4)))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(~(((((![X: $int, Y: $int] : ((f(X) = f(Y)) => (X = Y)) & $less(6, f(3))) & $less(f(3), 9)) & $less(6, f(4))) & $less(f(4), 9)) => ($lesseq(f(5), 6) | $lesseq(9, f(5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','injective_f_pigeonhole')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~($lesseq(f(5), 6) | $lesseq(9, f(5)) | (~(![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y)) & (~$lesseq(f(3), 6)) & (~$lesseq(9, f(3))) & (~$lesseq(f(4), 6)) & (~$lesseq(9, f(4))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y)) & (~$lesseq(f(3), 6)) & (~$lesseq(9, f(3))) & (~$lesseq(f(4), 6)) & (~$lesseq(9, f(4)))),
% 0.13/0.39 inference(or_elim,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~$lesseq(9, f(3))),
% 0.13/0.39 inference(and_elim,[status(thm)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~$lesseq(9, f(3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~$greatereq(f(3), 9)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~$lesseq(f(5), 6)) <=> (~$lesseq(f(5), 6))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~$lesseq(f(5), 6)),
% 0.13/0.39 inference(or_elim,[status(thm)],[5])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~$lesseq(f(5), 6)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ((~$lesseq(9, f(5))) <=> (~$greatereq(f(5), 9))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~$lesseq(9, f(5))) <=> (~$lesseq(9, f(5)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~$lesseq(9, f(5))),
% 0.13/0.39 inference(or_elim,[status(thm)],[5])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~$lesseq(9, f(5))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~$greatereq(f(5), 9)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.39 tff(18,assumption,(~$greatereq($sum(f(3), $product(-1, f(5))), 0)), introduced(assumption)).
% 0.13/0.39 tff(19,assumption,(~$lesseq($sum(f(3), $product(-1, f(4))), 0)), introduced(assumption)).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~$lesseq(f(4), 6)) <=> (~$lesseq(f(4), 6))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (~$lesseq(f(4), 6)),
% 0.13/0.39 inference(and_elim,[status(thm)],[6])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (~$lesseq(f(4), 6)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[18, 22, 19, 17])).
% 0.13/0.39 tff(24,plain,($lesseq($sum(f(3), $product(-1, f(4))), 0) | $greatereq($sum(f(3), $product(-1, f(5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ($lesseq($sum(f(3), $product(-1, f(4))), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (^[X: $int, Y: $int] : refl(((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0)) <=> ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0)) <=> ![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (^[X: $int, Y: $int] : rewrite(((~($sum(f(X), $product(-1, f(Y))) = 0)) | ($sum(X, $product(-1, Y)) = 0)) <=> ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~($sum(f(X), $product(-1, f(Y))) = 0)) | ($sum(X, $product(-1, Y)) = 0)) <=> ![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (^[X: $int, Y: $int] : rewrite(((~(f(X) = f(Y))) | (X = Y)) <=> ((~($sum(f(X), $product(-1, f(Y))) = 0)) | ($sum(X, $product(-1, Y)) = 0)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![X: $int, Y: $int] : ((~($sum(f(X), $product(-1, f(Y))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y)) <=> ![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.13/0.39 inference(and_elim,[status(thm)],[6])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~(f(X) = f(Y))) | (X = Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~($sum(f(X), $product(-1, f(Y))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.13/0.39 tff(37,plain,(
% 0.13/0.39 ![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(skolemize,[status(sab)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(4))) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(4))) = 0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (((~($sum(f(3), $product(-1, f(4))) = 0)) | $false) <=> (~($sum(f(3), $product(-1, f(4))) = 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ((1 = 0) <=> $false),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ($sum(4, -3) = 1),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ($product(-1, 3) = -3),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 ($sum(4, $product(-1, 3)) = $sum(4, -3)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 ($sum(4, $product(-1, 3)) = 1),
% 0.13/0.39 inference(transitivity,[status(thm)],[44, 42])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (($sum(4, $product(-1, 3)) = 0) <=> (1 = 0)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (($sum(4, $product(-1, 3)) = 0) <=> $false),
% 0.13/0.39 inference(transitivity,[status(thm)],[46, 41])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (((~($sum(f(3), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 3)) = 0)) <=> ((~($sum(f(3), $product(-1, f(4))) = 0)) | $false)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (((~($sum(f(3), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 3)) = 0)) <=> (~($sum(f(3), $product(-1, f(4))) = 0))),
% 0.13/0.39 inference(transitivity,[status(thm)],[48, 40])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(3), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 3)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(4))) = 0)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(3), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 3)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(4))) = 0)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[50, 39])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(3), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 3)) = 0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(4))) = 0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (~($sum(f(3), $product(-1, f(4))) = 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 38])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (($sum(f(3), $product(-1, f(4))) = 0) | (~$lesseq($sum(f(3), $product(-1, f(4))), 0)) | (~$greatereq($sum(f(3), $product(-1, f(4))), 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((~$lesseq($sum(f(3), $product(-1, f(4))), 0)) | (~$greatereq($sum(f(3), $product(-1, f(4))), 0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (~$greatereq($sum(f(3), $product(-1, f(4))), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[56, 25])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 ((~$lesseq(f(3), 6)) <=> (~$lesseq(f(3), 6))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (~$lesseq(f(3), 6)),
% 0.13/0.39 inference(and_elim,[status(thm)],[6])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (~$lesseq(f(3), 6)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((~$lesseq(9, f(4))) <=> (~$greatereq(f(4), 9))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~$lesseq(9, f(4))) <=> (~$lesseq(9, f(4)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (~$lesseq(9, f(4))),
% 0.13/0.39 inference(and_elim,[status(thm)],[6])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (~$lesseq(9, f(4))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 (~$greatereq(f(4), 9)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 ($lesseq($sum(f(4), $product(-1, f(5))), 0) | $greatereq(f(4), 9) | $lesseq(f(3), 6) | $greatereq($sum(f(3), $product(-1, f(5))), 0)),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 ($lesseq($sum(f(4), $product(-1, f(5))), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[66, 18, 65, 60])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(4), $product(-1, f(5))) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(4), $product(-1, f(5))) = 0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (((~($sum(f(4), $product(-1, f(5))) = 0)) | $false) <=> (~($sum(f(4), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 ((-1 = 0) <=> $false),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 ($sum(4, -5) = -1),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 ($product(-1, 5) = -5),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 ($sum(4, $product(-1, 5)) = $sum(4, -5)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 ($sum(4, $product(-1, 5)) = -1),
% 0.13/0.39 inference(transitivity,[status(thm)],[73, 71])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (($sum(4, $product(-1, 5)) = 0) <=> (-1 = 0)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.13/0.39 tff(76,plain,
% 0.13/0.39 (($sum(4, $product(-1, 5)) = 0) <=> $false),
% 0.13/0.39 inference(transitivity,[status(thm)],[75, 70])).
% 0.13/0.39 tff(77,plain,
% 0.13/0.39 ((~($sum(f(5), $product(-1, f(4))) = 0)) <=> (~($sum(f(4), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(78,plain,
% 0.13/0.39 (((~($sum(f(5), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 5)) = 0)) <=> ((~($sum(f(4), $product(-1, f(5))) = 0)) | $false)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[77, 76])).
% 0.13/0.39 tff(79,plain,
% 0.13/0.39 (((~($sum(f(5), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 5)) = 0)) <=> (~($sum(f(4), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(transitivity,[status(thm)],[78, 69])).
% 0.13/0.39 tff(80,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 5)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(4), $product(-1, f(5))) = 0)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[79])).
% 0.13/0.39 tff(81,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 5)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(4), $product(-1, f(5))) = 0)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[80, 68])).
% 0.13/0.39 tff(82,plain,
% 0.13/0.39 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(4))) = 0)) | ($sum(4, $product(-1, 5)) = 0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(83,plain,
% 0.13/0.39 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(4), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.13/0.39 tff(84,plain,
% 0.13/0.39 (~($sum(f(4), $product(-1, f(5))) = 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[83, 38])).
% 0.13/0.39 tff(85,plain,
% 0.13/0.39 (($sum(f(4), $product(-1, f(5))) = 0) | (~$lesseq($sum(f(4), $product(-1, f(5))), 0)) | (~$greatereq($sum(f(4), $product(-1, f(5))), 0))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(86,plain,
% 0.13/0.39 ((~$lesseq($sum(f(4), $product(-1, f(5))), 0)) | (~$greatereq($sum(f(4), $product(-1, f(5))), 0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.13/0.39 tff(87,plain,
% 0.13/0.39 (~$greatereq($sum(f(4), $product(-1, f(5))), 0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[86, 67])).
% 0.13/0.39 tff(88,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[60, 87, 57, 17])).
% 0.13/0.39 tff(89,plain,($greatereq($sum(f(3), $product(-1, f(5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(90,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(5))) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(5))) = 0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(91,plain,
% 0.13/0.39 (((~($sum(f(3), $product(-1, f(5))) = 0)) | $false) <=> (~($sum(f(3), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(92,plain,
% 0.13/0.39 ((-2 = 0) <=> $false),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(93,plain,
% 0.13/0.39 ($sum(3, -5) = -2),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(94,plain,
% 0.13/0.39 ($sum(3, $product(-1, 5)) = $sum(3, -5)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.13/0.39 tff(95,plain,
% 0.13/0.39 ($sum(3, $product(-1, 5)) = -2),
% 0.13/0.39 inference(transitivity,[status(thm)],[94, 93])).
% 0.13/0.39 tff(96,plain,
% 0.13/0.39 (($sum(3, $product(-1, 5)) = 0) <=> (-2 = 0)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[95])).
% 0.13/0.39 tff(97,plain,
% 0.13/0.39 (($sum(3, $product(-1, 5)) = 0) <=> $false),
% 0.13/0.39 inference(transitivity,[status(thm)],[96, 92])).
% 0.13/0.39 tff(98,plain,
% 0.13/0.39 ((~($sum(f(5), $product(-1, f(3))) = 0)) <=> (~($sum(f(3), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(99,plain,
% 0.13/0.39 (((~($sum(f(5), $product(-1, f(3))) = 0)) | ($sum(3, $product(-1, 5)) = 0)) <=> ((~($sum(f(3), $product(-1, f(5))) = 0)) | $false)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[98, 97])).
% 0.13/0.39 tff(100,plain,
% 0.13/0.39 (((~($sum(f(5), $product(-1, f(3))) = 0)) | ($sum(3, $product(-1, 5)) = 0)) <=> (~($sum(f(3), $product(-1, f(5))) = 0))),
% 0.13/0.39 inference(transitivity,[status(thm)],[99, 91])).
% 0.13/0.39 tff(101,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(3))) = 0)) | ($sum(3, $product(-1, 5)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(5))) = 0)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[100])).
% 0.13/0.39 tff(102,plain,
% 0.13/0.39 (((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(3))) = 0)) | ($sum(3, $product(-1, 5)) = 0))) <=> ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(5))) = 0)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[101, 90])).
% 0.13/0.40 tff(103,plain,
% 0.13/0.40 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | ((~($sum(f(5), $product(-1, f(3))) = 0)) | ($sum(3, $product(-1, 5)) = 0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(104,plain,
% 0.13/0.40 ((~![X: $int, Y: $int] : ((~($sum(f(Y), $product(-1, f(X))) = 0)) | ($sum(X, $product(-1, Y)) = 0))) | (~($sum(f(3), $product(-1, f(5))) = 0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.13/0.40 tff(105,plain,
% 0.13/0.40 (~($sum(f(3), $product(-1, f(5))) = 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[104, 38])).
% 0.13/0.40 tff(106,plain,
% 0.13/0.40 (($sum(f(3), $product(-1, f(5))) = 0) | (~$lesseq($sum(f(3), $product(-1, f(5))), 0)) | (~$greatereq($sum(f(3), $product(-1, f(5))), 0))),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(107,plain,
% 0.13/0.40 ((~$lesseq($sum(f(3), $product(-1, f(5))), 0)) | (~$greatereq($sum(f(3), $product(-1, f(5))), 0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.13/0.40 tff(108,plain,
% 0.13/0.40 (~$lesseq($sum(f(3), $product(-1, f(5))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[107, 89])).
% 0.13/0.40 tff(109,plain,
% 0.13/0.40 ($greatereq($sum(f(3), $product(-1, f(4))), 0) | $greatereq(f(4), 9) | $lesseq(f(5), 6) | $lesseq($sum(f(3), $product(-1, f(5))), 0)),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40 tff(110,plain,
% 0.13/0.40 ($greatereq($sum(f(3), $product(-1, f(4))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[109, 65, 108, 12])).
% 0.13/0.40 tff(111,plain,
% 0.13/0.40 (~$lesseq($sum(f(3), $product(-1, f(4))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 110])).
% 0.13/0.40 tff(112,assumption,(~$greatereq($sum(f(4), $product(-1, f(5))), 0)), introduced(assumption)).
% 0.13/0.40 tff(113,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[108, 22, 112, 9])).
% 0.13/0.40 tff(114,plain,($greatereq($sum(f(4), $product(-1, f(5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(115,plain,
% 0.13/0.40 (~$lesseq($sum(f(4), $product(-1, f(5))), 0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[86, 114])).
% 0.13/0.40 tff(116,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(theory_lemma,[status(thm)],[12, 115, 111, 9])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------