TSTP Solution File: ARI634_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI634_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 17:02:23 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 : ARI634_1 : TPTP v8.1.0. Released v6.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 : Tue Aug 30 01:15:58 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(w_type, type, (
% 0.13/0.39 w: $real)).
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: $real > $real)).
% 0.13/0.39 tff(x_type, type, (
% 0.13/0.39 x: $real)).
% 0.13/0.39 tff(v_type, type, (
% 0.13/0.39 v: $real)).
% 0.13/0.39 tff(u_type, type, (
% 0.13/0.39 u: $real)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~$lesseq($sum(v, $product(-1, u)), 0)) <=> (~$greatereq($sum(u, $product(-1, v)), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~$lesseq(v, u)) <=> (~$lesseq($sum(v, $product(-1, u)), 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~$lesseq(v, u)) <=> (~$lesseq(v, u))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ($less(u, v) <=> (~$lesseq(v, u))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,($less(u, v)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hypothesis')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~$lesseq(v, u)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~$lesseq(v, u)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~$lesseq($sum(v, $product(-1, u)), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~$greatereq($sum(u, $product(-1, v)), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ($lesseq($sum($product(-1, u), $sum(v, $sum($product(2, w), $product(-1, $product(w, f(x)))))), 0) <=> $greatereq($sum(u, $sum($product(-1, v), $sum($product(-2, w), $product(w, f(x))))), 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 ($sum(v, $sum(w, $sum($product(-1, u), $sum(w, $product(-1, $product(w, f(x))))))) = $sum($product(-1, u), $sum(v, $sum($product(2, w), $product(-1, $product(w, f(x))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ($sum($product(-1, $product(-1, w)), $product(-1, $product(w, f(x)))) = $sum(w, $product(-1, $product(w, f(x))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 ($product(-1, $sum($product(-1, w), $product(w, f(x)))) = $sum($product(-1, $product(-1, w)), $product(-1, $product(w, f(x))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ($sum($product(w, -1), $product(w, f(x))) = $sum($product(-1, w), $product(w, f(x)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 ($product(w, $sum(-1, f(x))) = $sum($product(w, -1), $product(w, f(x)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ($product(w, $sum(-1, f(x))) = $sum($product(-1, w), $product(w, f(x)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[15, 14])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ($product(-1, $product(w, $sum(-1, f(x)))) = $product(-1, $sum($product(-1, w), $product(w, f(x))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ($product(-1, $product(w, $sum(-1, f(x)))) = $sum($product(-1, $product(-1, w)), $product(-1, $product(w, f(x))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[17, 13])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ($product(-1, $product(w, $sum(-1, f(x)))) = $sum(w, $product(-1, $product(w, f(x))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[18, 12])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))) = $sum(v, $sum(w, $sum($product(-1, u), $sum(w, $product(-1, $product(w, f(x)))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))) = $sum($product(-1, u), $sum(v, $sum($product(2, w), $product(-1, $product(w, f(x))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[20, 11])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))), 0) <=> $lesseq($sum($product(-1, u), $sum(v, $sum($product(2, w), $product(-1, $product(w, f(x)))))), 0)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))), 0) <=> $greatereq($sum(u, $sum($product(-1, v), $sum($product(-2, w), $product(w, f(x))))), 0)),
% 0.13/0.39 inference(transitivity,[status(thm)],[22, 10])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ($lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x))))) <=> $lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))), 0)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ($lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x))))) <=> $lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~(~$lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x))))))) <=> $lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ($less($sum(u, $product(w, $sum(-1, f(x)))), $sum(v, w)) <=> (~$lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~$less($sum(u, $product(w, $sum(-1, f(x)))), $sum(v, w))) <=> (~(~$lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~$less($sum(u, $product(w, $sum(-1, f(x)))), $sum(v, w))) <=> $lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.13/0.39 tff(30,axiom,(~$less($sum(u, $product(w, $sum(-1, f(x)))), $sum(v, w))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion')).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ($lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ($lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ($lesseq($sum(v, w), $sum(u, $product(w, $sum(-1, f(x)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, $sum(-1, f(x))))))), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 24])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ($greatereq($sum(u, $sum($product(-1, v), $sum($product(-2, w), $product(w, f(x))))), 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[34, 23])).
% 0.13/0.39 tff(36,assumption,($lesseq($sum($product(w, f(x)), $product(-2, w)), 0)), introduced(assumption)).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[36, 35, 9])).
% 0.13/0.39 tff(38,plain,(~$lesseq($sum($product(w, f(x)), $product(-2, w)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (^[X: $real] : refl($lesseq(f(X), 2) <=> $lesseq(f(X), 2))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X: $real] : $lesseq(f(X), 2) <=> ![X: $real] : $lesseq(f(X), 2)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (![X: $real] : $lesseq(f(X), 2) <=> ![X: $real] : $lesseq(f(X), 2)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,axiom,(![X: $real] : $lesseq(f(X), 2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f_less_equal_2')).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![X: $real] : $lesseq(f(X), 2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,(
% 0.13/0.39 ![X: $real] : $lesseq(f(X), 2)),
% 0.13/0.39 inference(skolemize,[status(sab)],[43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $real] : $lesseq(f(X), 2)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 ((~![X: $real] : $lesseq(f(X), 2)) | $lesseq(f(x), 2)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 ($lesseq(f(x), 2)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((~$lesseq(w, 0)) <=> (~$lesseq(w, 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ($greater(w, 0) <=> (~$lesseq(w, 0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(50,axiom,($greater(w, 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','hypothesis_01')).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (~$lesseq(w, 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 (~$lesseq(w, 0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 48])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ($lesseq($sum($product(w, f(x)), $product(-2, w)), 0) | $lesseq(w, 0) | (~$lesseq(f(x), 2))),
% 0.13/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 52, 47, 38])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------