TSTP Solution File: ARI691_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI691_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 17:02:37 EDT 2022
% Result : Theorem 0.14s 0.37s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI691_1 : TPTP v8.1.0. Released v6.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Aug 30 01:43:41 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.33 Usage: tptp [options] [-file:]file
% 0.14/0.33 -h, -? prints this message.
% 0.14/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.33 -m, -model generate model.
% 0.14/0.33 -p, -proof generate proof.
% 0.14/0.33 -c, -core generate unsat core of named formulas.
% 0.14/0.33 -st, -statistics display statistics.
% 0.14/0.33 -t:timeout set timeout (in second).
% 0.14/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.33 -<param>:<value> configuration parameter and value.
% 0.14/0.33 -o:<output-file> file to place output in.
% 0.14/0.37 % SZS status Theorem
% 0.14/0.37 % SZS output start Proof
% 0.14/0.37 tff(f_type, type, (
% 0.14/0.37 f: $int > $int)).
% 0.14/0.37 tff(k!0_type, type, (
% 0.14/0.37 k!0: $int)).
% 0.14/0.37 tff(b_type, type, (
% 0.14/0.37 b: $int)).
% 0.14/0.37 tff(a_type, type, (
% 0.14/0.37 a: $int)).
% 0.14/0.37 tff(1,plain,
% 0.14/0.37 ((k!0 = f(k!0)) <=> ($sum(k!0, $product(-1, f(k!0))) = 0)),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(2,plain,
% 0.14/0.37 (($product(a, b) = f($product(a, b))) <=> (k!0 = f(k!0))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(3,plain,
% 0.14/0.37 (($product(a, b) = f($product(a, b))) <=> ($product(a, b) = f($product(a, b)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(4,axiom,($product(a, b) = f($product(a, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','eq')).
% 0.14/0.37 tff(5,plain,
% 0.14/0.37 ($product(a, b) = f($product(a, b))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.37 tff(6,plain,
% 0.14/0.37 (k!0 = f(k!0)),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.14/0.37 tff(7,plain,
% 0.14/0.37 ($sum(k!0, $product(-1, f(k!0))) = 0),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.37 tff(8,plain,
% 0.14/0.37 ((~($sum(k!0, $product(-1, f(k!0))) = 0)) | $lesseq($sum(k!0, $product(-1, f(k!0))), 0)),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.37 tff(9,plain,
% 0.14/0.37 ($lesseq($sum(k!0, $product(-1, f(k!0))), 0)),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.37 tff(10,plain,
% 0.14/0.37 ((~($sum(k!0, $product(-1, f(k!0))) = 0)) | $greatereq($sum(k!0, $product(-1, f(k!0))), 0)),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.37 tff(11,plain,
% 0.14/0.37 ($greatereq($sum(k!0, $product(-1, f(k!0))), 0)),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.14/0.37 tff(12,plain,
% 0.14/0.37 (k!0 = f(k!0)),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[11, 9])).
% 0.14/0.37 tff(13,plain,
% 0.14/0.37 (f(k!0) = k!0),
% 0.14/0.37 inference(symmetry,[status(thm)],[12])).
% 0.14/0.37 tff(14,plain,
% 0.14/0.37 (f(f(k!0)) = f(k!0)),
% 0.14/0.37 inference(monotonicity,[status(thm)],[13])).
% 0.14/0.37 tff(15,plain,
% 0.14/0.37 (f(k!0) = f(f(k!0))),
% 0.14/0.37 inference(symmetry,[status(thm)],[14])).
% 0.14/0.37 tff(16,assumption,(~$lesseq($sum(k!0, $product(-1, f(f(k!0)))), 0)), introduced(assumption)).
% 0.14/0.37 tff(17,plain,
% 0.14/0.37 ($false),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[16, 9, 15])).
% 0.14/0.37 tff(18,plain,($lesseq($sum(k!0, $product(-1, f(f(k!0)))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.37 tff(19,plain,
% 0.14/0.37 ((~($sum(f(f(k!0)), $product(-1, k!0)) = 0)) <=> (~($sum(k!0, $product(-1, f(f(k!0)))) = 0))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(20,plain,
% 0.14/0.37 ((~(f(f(k!0)) = k!0)) <=> (~($sum(f(f(k!0)), $product(-1, k!0)) = 0))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(21,plain,
% 0.14/0.37 ((~(f(f($product(a, b))) = $product(a, b))) <=> (~(f(f(k!0)) = k!0))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(22,plain,
% 0.14/0.37 ((~(f(f($product(a, b))) = $product(a, b))) <=> (~(f(f($product(a, b))) = $product(a, b)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(23,plain,
% 0.14/0.37 ((~(f(f($product(a, b))) = $product(b, a))) <=> (~(f(f($product(a, b))) = $product(a, b)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(24,axiom,(~(f(f($product(a, b))) = $product(b, a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.14/0.37 tff(25,plain,
% 0.14/0.37 (~(f(f($product(a, b))) = $product(a, b))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.14/0.37 tff(26,plain,
% 0.14/0.37 (~(f(f($product(a, b))) = $product(a, b))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.14/0.37 tff(27,plain,
% 0.14/0.37 (~(f(f(k!0)) = k!0)),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.14/0.37 tff(28,plain,
% 0.14/0.37 (~($sum(f(f(k!0)), $product(-1, k!0)) = 0)),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.14/0.37 tff(29,plain,
% 0.14/0.37 (~($sum(k!0, $product(-1, f(f(k!0)))) = 0)),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.14/0.37 tff(30,plain,
% 0.14/0.37 (($sum(k!0, $product(-1, f(f(k!0)))) = 0) | (~$lesseq($sum(k!0, $product(-1, f(f(k!0)))), 0)) | (~$greatereq($sum(k!0, $product(-1, f(f(k!0)))), 0))),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[])).
% 0.14/0.37 tff(31,plain,
% 0.14/0.37 ((~$lesseq($sum(k!0, $product(-1, f(f(k!0)))), 0)) | (~$greatereq($sum(k!0, $product(-1, f(f(k!0)))), 0))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.14/0.37 tff(32,plain,
% 0.14/0.37 (~$greatereq($sum(k!0, $product(-1, f(f(k!0)))), 0)),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[31, 18])).
% 0.14/0.37 tff(33,plain,
% 0.14/0.37 ($false),
% 0.14/0.37 inference(theory_lemma,[status(thm)],[32, 11, 15])).
% 0.14/0.37 % SZS output end Proof
%------------------------------------------------------------------------------