TSTP Solution File: ARI633_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI633_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI633_1 : TPTP v8.1.0. Released v6.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 01:13:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(w_type, type, (
% 0.19/0.38 w: $real)).
% 0.19/0.38 tff(f_type, type, (
% 0.19/0.38 f: $real > $real)).
% 0.19/0.38 tff(x_type, type, (
% 0.19/0.38 x: $real)).
% 0.19/0.38 tff(v_type, type, (
% 0.19/0.38 v: $real)).
% 0.19/0.38 tff(u_type, type, (
% 0.19/0.38 u: $real)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((0 = $sum($product(w, f(x)), $product(-1, w))) <=> ($sum($product(w, f(x)), $product(-1, w)) = 0)),
% 0.19/0.38 inference(commutativity,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (($sum($product(w, f(x)), $product(-1, w)) = 0) <=> (0 = $sum($product(w, f(x)), $product(-1, w)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[1])).
% 0.19/0.38 tff(3,assumption,(~$greatereq(f(x), 1)), introduced(assumption)).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 ($lesseq($sum($product(-1, u), $sum(v, $sum(w, $product(-1, $product(w, f(x)))))), 0) <=> $greatereq($sum(u, $sum($product(-1, v), $sum($product(-1, w), $product(w, f(x))))), 0)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 ($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, f(x)))))) = $sum($product(-1, u), $sum(v, $sum(w, $product(-1, $product(w, f(x))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, f(x)))))), 0) <=> $lesseq($sum($product(-1, u), $sum(v, $sum(w, $product(-1, $product(w, f(x)))))), 0)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, f(x)))))), 0) <=> $greatereq($sum(u, $sum($product(-1, v), $sum($product(-1, w), $product(w, f(x))))), 0)),
% 0.19/0.38 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ($lesseq($sum(v, w), $sum(u, $product(w, f(x)))) <=> $lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, f(x)))))), 0)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ($lesseq($sum(v, w), $sum(u, $product(w, f(x)))) <=> $lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ((~(~$lesseq($sum(v, w), $sum(u, $product(w, f(x)))))) <=> $lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ($less($sum(u, $product(w, f(x))), $sum(v, w)) <=> (~$lesseq($sum(v, w), $sum(u, $product(w, f(x)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 ((~$less($sum(u, $product(w, f(x))), $sum(v, w))) <=> (~(~$lesseq($sum(v, w), $sum(u, $product(w, f(x))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[11])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~$less($sum(u, $product(w, f(x))), $sum(v, w))) <=> $lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[12, 10])).
% 0.19/0.38 tff(14,axiom,(~$less($sum(u, $product(w, f(x))), $sum(v, w))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion')).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ($lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ($lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ($lesseq($sum(v, w), $sum(u, $product(w, f(x))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 ($lesseq($sum(v, $sum(w, $sum($product(-1, u), $product(-1, $product(w, f(x)))))), 0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 8])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ($greatereq($sum(u, $sum($product(-1, v), $sum($product(-1, w), $product(w, f(x))))), 0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 7])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ((~$lesseq(w, 0)) <=> (~$lesseq(w, 0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ($greater(w, 0) <=> (~$lesseq(w, 0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,axiom,($greater(w, 0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis_01')).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (~$lesseq(w, 0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (~$lesseq(w, 0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((~$lesseq($sum(v, $product(-1, u)), 0)) <=> (~$greatereq($sum(u, $product(-1, v)), 0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~$lesseq(v, u)) <=> (~$lesseq($sum(v, $product(-1, u)), 0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 ((~$lesseq(v, u)) <=> (~$lesseq(v, u))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 ($less(u, v) <=> (~$lesseq(v, u))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,axiom,($less(u, v)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','hypothesis')).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (~$lesseq(v, u)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~$lesseq(v, u)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~$lesseq($sum(v, $product(-1, u)), 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (~$greatereq($sum(u, $product(-1, v)), 0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ($greatereq(f(x), 1) | $greatereq($sum(u, $product(-1, v)), 0) | $lesseq(w, 0) | (~$greatereq($sum(u, $sum($product(-1, v), $sum($product(-1, w), $product(w, f(x))))), 0))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 33, 24, 19, 3])).
% 0.19/0.39 tff(36,plain,($greatereq(f(x), 1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (^[X: $real] : refl($lesseq(f(X), 1) <=> $lesseq(f(X), 1))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![X: $real] : $lesseq(f(X), 1) <=> ![X: $real] : $lesseq(f(X), 1)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X: $real] : $lesseq(f(X), 1) <=> ![X: $real] : $lesseq(f(X), 1)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(40,axiom,(![X: $real] : $lesseq(f(X), 1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f_less_equal_1')).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![X: $real] : $lesseq(f(X), 1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.39 tff(42,plain,(
% 0.19/0.39 ![X: $real] : $lesseq(f(X), 1)),
% 0.19/0.39 inference(skolemize,[status(sab)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![X: $real] : $lesseq(f(X), 1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![X: $real] : $lesseq(f(X), 1)) | $lesseq(f(x), 1)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ($lesseq(f(x), 1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (($sum($product(w, f(x)), $product(-1, w)) = 0) | (~$greatereq(f(x), 1)) | (~$lesseq(f(x), 1))),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ($sum($product(w, f(x)), $product(-1, w)) = 0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[46, 45, 36])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (0 = $sum($product(w, f(x)), $product(-1, w))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 2])).
% 0.19/0.39 tff(49,assumption,(~(0 = $sum($product(w, f(x)), $product(-1, w)))), introduced(assumption)).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,(0 = $sum($product(w, f(x)), $product(-1, w))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(52,assumption,($lesseq($sum($product(w, f(x)), $product(-1, w)), 0)), introduced(assumption)).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[52, 19, 33])).
% 0.19/0.39 tff(54,plain,(~$lesseq($sum($product(w, f(x)), $product(-1, w)), 0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~(0 = $sum($product(w, f(x)), $product(-1, w)))) | $lesseq($sum($product(w, f(x)), $product(-1, w)), 0)),
% 0.19/0.39 inference(theory_lemma,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (~(0 = $sum($product(w, f(x)), $product(-1, w)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------