TSTP Solution File: ARI186_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI186_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 17:00:52 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ARI186_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 22:19:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(g_type, type, (
% 0.14/0.40 g: ( $int * $int ) > $int)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[U: $int, V: $int] : refl(($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0) <=> ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0) <=> ![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (^[U: $int, V: $int] : rewrite((g(U, V) = g(U, $sum(2, V))) <=> ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V))) <=> ![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)),
% 0.14/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V))) <=> ![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 ((~(![U: $int, V: $int] : (g(U, V) = g(U, $sum(V, 2))) => ((g(3, 3) = g(3, 4)) => (g(3, 2) = g(3, 5))))) <=> (~((g(3, 2) = g(3, 5)) | (~(g(3, 3) = g(3, 4))) | (~![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(7,axiom,(~(![U: $int, V: $int] : (g(U, V) = g(U, $sum(V, 2))) => ((g(3, 3) = g(3, 4)) => (g(3, 2) = g(3, 5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (~((g(3, 2) = g(3, 5)) | (~(g(3, 3) = g(3, 4))) | (~![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[8])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![U: $int, V: $int] : (g(U, V) = g(U, $sum(2, V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.14/0.40 tff(12,plain,(
% 0.14/0.40 ![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)),
% 0.14/0.40 inference(skolemize,[status(sab)],[11])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, 5))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, 5))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (($sum(g(3, 3), $product(-1, g(3, $sum(2, 3)))) = 0) <=> ($sum(g(3, 3), $product(-1, g(3, 5))) = 0)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, $sum(2, 3)))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, 5))) = 0))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, $sum(2, 3)))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, 5))) = 0))),
% 0.14/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, $sum(2, 3)))) = 0)),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 3), $product(-1, g(3, 5))) = 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 ($sum(g(3, 3), $product(-1, g(3, 5))) = 0),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 ((~($sum(g(3, 3), $product(-1, g(3, 5))) = 0)) | $lesseq($sum(g(3, 3), $product(-1, g(3, 5))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ($lesseq($sum(g(3, 3), $product(-1, g(3, 5))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 ((~($sum(g(3, 3), $product(-1, g(3, 5))) = 0)) | $greatereq($sum(g(3, 3), $product(-1, g(3, 5))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 ($greatereq($sum(g(3, 3), $product(-1, g(3, 5))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.14/0.40 tff(25,assumption,(~$greatereq($sum(g(3, 2), $product(-1, g(3, 5))), 0)), introduced(assumption)).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 4), $product(-1, g(3, 2))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 4), $product(-1, g(3, 2))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (($sum($product(-1, g(3, 4)), g(3, 2)) = 0) <=> ($sum(g(3, 4), $product(-1, g(3, 2))) = 0)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 ($sum(g(3, 2), $product(-1, g(3, 4))) = $sum($product(-1, g(3, 4)), g(3, 2))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 ($product(-1, g(3, $sum(2, 2))) = $product(-1, g(3, 4))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 ($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = $sum(g(3, 2), $product(-1, g(3, 4)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[29])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 ($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = $sum($product(-1, g(3, 4)), g(3, 2))),
% 0.14/0.40 inference(transitivity,[status(thm)],[30, 28])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = 0) <=> ($sum($product(-1, g(3, 4)), g(3, 2)) = 0)),
% 0.14/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = 0) <=> ($sum(g(3, 4), $product(-1, g(3, 2))) = 0)),
% 0.14/0.40 inference(transitivity,[status(thm)],[32, 27])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 4), $product(-1, g(3, 2))) = 0))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = 0)) <=> ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 4), $product(-1, g(3, 2))) = 0))),
% 0.14/0.40 inference(transitivity,[status(thm)],[34, 26])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 2), $product(-1, g(3, $sum(2, 2)))) = 0)),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~![U: $int, V: $int] : ($sum(g(U, V), $product(-1, g(U, $sum(2, V)))) = 0)) | ($sum(g(3, 4), $product(-1, g(3, 2))) = 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 ($sum(g(3, 4), $product(-1, g(3, 2))) = 0),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[37, 13])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 ((~($sum(g(3, 4), $product(-1, g(3, 2))) = 0)) | $lesseq($sum(g(3, 4), $product(-1, g(3, 2))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ($lesseq($sum(g(3, 4), $product(-1, g(3, 2))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 ((g(3, 3) = g(3, 4)) <=> ($sum(g(3, 3), $product(-1, g(3, 4))) = 0)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 ((g(3, 3) = g(3, 4)) <=> (g(3, 3) = g(3, 4))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (g(3, 3) = g(3, 4)),
% 0.14/0.40 inference(or_elim,[status(thm)],[8])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (g(3, 3) = g(3, 4)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ($sum(g(3, 3), $product(-1, g(3, 4))) = 0),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 ((~($sum(g(3, 3), $product(-1, g(3, 4))) = 0)) | $lesseq($sum(g(3, 3), $product(-1, g(3, 4))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 ($lesseq($sum(g(3, 3), $product(-1, g(3, 4))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[47, 40, 25, 24])).
% 0.14/0.40 tff(49,plain,($greatereq($sum(g(3, 2), $product(-1, g(3, 5))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 ((~(g(3, 2) = g(3, 5))) <=> (~($sum(g(3, 2), $product(-1, g(3, 5))) = 0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 ((~(g(3, 2) = g(3, 5))) <=> (~(g(3, 2) = g(3, 5)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (~(g(3, 2) = g(3, 5))),
% 0.14/0.40 inference(or_elim,[status(thm)],[8])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (~(g(3, 2) = g(3, 5))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (~($sum(g(3, 2), $product(-1, g(3, 5))) = 0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (($sum(g(3, 2), $product(-1, g(3, 5))) = 0) | (~$lesseq($sum(g(3, 2), $product(-1, g(3, 5))), 0)) | (~$greatereq($sum(g(3, 2), $product(-1, g(3, 5))), 0))),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 ((~$lesseq($sum(g(3, 2), $product(-1, g(3, 5))), 0)) | (~$greatereq($sum(g(3, 2), $product(-1, g(3, 5))), 0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (~$lesseq($sum(g(3, 2), $product(-1, g(3, 5))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[56, 49])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 ((~($sum(g(3, 4), $product(-1, g(3, 2))) = 0)) | $greatereq($sum(g(3, 4), $product(-1, g(3, 2))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 ($greatereq($sum(g(3, 4), $product(-1, g(3, 2))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[58, 38])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 ((~($sum(g(3, 3), $product(-1, g(3, 4))) = 0)) | $greatereq($sum(g(3, 3), $product(-1, g(3, 4))), 0)),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 ($greatereq($sum(g(3, 3), $product(-1, g(3, 4))), 0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[60, 45])).
% 0.14/0.40 tff(62,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(theory_lemma,[status(thm)],[61, 59, 57, 22])).
% 0.14/0.40 % SZS output end Proof
%------------------------------------------------------------------------------