TSTP Solution File: ARI180_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI180_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 17:00:51 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ARI180_1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.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 : Mon Aug 29 22:26:26 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $int > $int)).
% 0.20/0.39 tff(tptp_fun_U_1_type, type, (
% 0.20/0.39 tptp_fun_U_1: $int)).
% 0.20/0.39 tff(tptp_fun_V_0_type, type, (
% 0.20/0.39 tptp_fun_V_0: $int)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((~((~(($sum(U!1, $sum(V!0, $product(-1, f(U!1)))) = 0) & ($sum(V!0, $product(-1, f(U!1))) = 0))) | ($sum(f(0), $product(-1, V!0)) = 0))) <=> (~((~(($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0) & ($sum(V!0, $product(-1, f(U!1))) = 0))) | ($sum(f(0), $product(-1, V!0)) = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0))) <=> (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 ((~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(V, $product(-1, f(0))) = 0))) <=> (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))) <=> (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(V, $product(-1, f(0))) = 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ((~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))) <=> (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~![U: $int, V: $int] : ((($sum(U, V) = f(U)) & ($difference(V, f(U)) = 0)) => (V = f(0)))) <=> (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,axiom,(~![U: $int, V: $int] : ((($sum(U, V) = f(U)) & ($difference(V, f(U)) = 0)) => (V = f(0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, V) = f(U)) & ($sum(V, $product(-1, f(U))) = 0))) | (V = f(0)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(V, $product(-1, f(0))) = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~![U: $int, V: $int] : ((~(($sum(U, $sum(V, $product(-1, f(U)))) = 0) & ($sum(V, $product(-1, f(U))) = 0))) | ($sum(f(0), $product(-1, V)) = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.20/0.39 tff(16,plain,(
% 0.20/0.39 ~((~(($sum(U!1, $sum(V!0, $product(-1, f(U!1)))) = 0) & ($sum(V!0, $product(-1, f(U!1))) = 0))) | ($sum(f(0), $product(-1, V!0)) = 0))),
% 0.20/0.39 inference(skolemize,[status(sab)],[15])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (~((~(($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0) & ($sum(V!0, $product(-1, f(U!1))) = 0))) | ($sum(f(0), $product(-1, V!0)) = 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0) & ($sum(V!0, $product(-1, f(U!1))) = 0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0),
% 0.20/0.39 inference(and_elim,[status(thm)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0)) | $lesseq($sum(V!0, $sum(U!1, $product(-1, f(U!1)))), 0)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ($lesseq($sum(V!0, $sum(U!1, $product(-1, f(U!1)))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = 0)) | $greatereq($sum(V!0, $sum(U!1, $product(-1, f(U!1)))), 0)),
% 0.20/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ($greatereq($sum(V!0, $sum(U!1, $product(-1, f(U!1)))), 0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ($sum(V!0, $product(-1, f(U!1))) = 0),
% 0.20/0.40 inference(and_elim,[status(thm)],[18])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~($sum(V!0, $product(-1, f(U!1))) = 0)) | $lesseq($sum(V!0, $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ($lesseq($sum(V!0, $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~($sum(V!0, $product(-1, f(U!1))) = 0)) | $greatereq($sum(V!0, $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ($greatereq($sum(V!0, $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (U!1 = $sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1))))))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[28, 26, 28, 26, 23, 21])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 ($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))) = U!1),
% 0.20/0.40 inference(symmetry,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))) = 0),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[28, 26])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (0 = $sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1))))))),
% 0.20/0.40 inference(symmetry,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (0 = U!1),
% 0.20/0.40 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (f(0) = f(U!1)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~(f(0) = f(U!1))) | $lesseq($sum(f(0), $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ($lesseq($sum(f(0), $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ($greatereq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0) | (~$lesseq($sum(V!0, $product(-1, f(U!1))), 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ($greatereq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 26])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ($lesseq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0) | (~$greatereq($sum(V!0, $product(-1, f(U!1))), 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ($lesseq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[39, 28])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((U!1 = $sum(V!0, $sum(U!1, $product(-1, f(U!1))))) | (~$lesseq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0)) | (~$greatereq($sum(U!1, $product(-1, $sum(V!0, $sum(U!1, $product(-1, f(U!1)))))), 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (U!1 = $sum(V!0, $sum(U!1, $product(-1, f(U!1))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 40, 38])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ($sum(V!0, $sum(U!1, $product(-1, f(U!1)))) = U!1),
% 0.20/0.40 inference(symmetry,[status(thm)],[42])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (0 = $sum(V!0, $sum(U!1, $product(-1, f(U!1))))),
% 0.20/0.40 inference(symmetry,[status(thm)],[19])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (0 = U!1),
% 0.20/0.40 inference(transitivity,[status(thm)],[44, 43])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (f(0) = f(U!1)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~(f(0) = f(U!1))) | $greatereq($sum(f(0), $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ($greatereq($sum(f(0), $product(-1, f(U!1))), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,assumption,(~$greatereq($sum(f(0), $product(-1, V!0)), 0)), introduced(assumption)).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[49, 26, 48])).
% 0.20/0.40 tff(51,plain,($greatereq($sum(f(0), $product(-1, V!0)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (~($sum(f(0), $product(-1, V!0)) = 0)),
% 0.20/0.40 inference(or_elim,[status(thm)],[17])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (($sum(f(0), $product(-1, V!0)) = 0) | (~$lesseq($sum(f(0), $product(-1, V!0)), 0)) | (~$greatereq($sum(f(0), $product(-1, V!0)), 0))),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 ((~$lesseq($sum(f(0), $product(-1, V!0)), 0)) | (~$greatereq($sum(f(0), $product(-1, V!0)), 0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (~$lesseq($sum(f(0), $product(-1, V!0)), 0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(theory_lemma,[status(thm)],[55, 28, 36])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------