TSTP Solution File: ARI182_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI182_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI182_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 22:38:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $int > $int)).
% 0.20/0.38 tff(tptp_fun_V_1_type, type, (
% 0.20/0.38 tptp_fun_V_1: $int)).
% 0.20/0.38 tff(tptp_fun_W_0_type, type, (
% 0.20/0.38 tptp_fun_W_0: $int)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2)) <=> (~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![V: $int, W: $int] : $greatereq($sum(f($sum(f(V), W)), $sum($product(-1, V), $product(-1, W))), 2)) <=> (~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 ((~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))) <=> (~![V: $int, W: $int] : $greatereq($sum(f($sum(f(V), W)), $sum($product(-1, V), $product(-1, W))), 2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))) <=> (~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~(![U: $int] : $greater(f(U), U) => ![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum($sum(V, W), 2)))) <=> (~((~![U: $int] : (~$lesseq(f(U), U))) | ![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,axiom,(~(![U: $int] : $greater(f(U), U) => ![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum($sum(V, W), 2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~((~![U: $int] : (~$lesseq(f(U), U))) | ![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $greatereq(f($sum(f(V), W)), $sum(2, $sum(V, W)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $greatereq($sum(f($sum(f(V), W)), $sum($product(-1, V), $product(-1, W))), 2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~![V: $int, W: $int] : $lesseq($sum(W, $sum(V, $product(-1, f($sum(W, f(V)))))), -2)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 1])).
% 0.20/0.38 tff(16,plain,(
% 0.20/0.38 ~$lesseq($sum(W!0, $sum(V!1, $product(-1, f($sum(W!0, f(V!1)))))), -2)),
% 0.20/0.38 inference(skolemize,[status(sab)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (^[U: $int] : refl((~$greatereq($sum(U, $product(-1, f(U))), 0)) <=> (~$greatereq($sum(U, $product(-1, f(U))), 0)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0)) <=> ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (^[U: $int] : rewrite((~$lesseq($sum(f(U), $product(-1, U)), 0)) <=> (~$greatereq($sum(U, $product(-1, f(U))), 0)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0)) <=> ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[U: $int] : rewrite((~$lesseq(f(U), U)) <=> (~$lesseq($sum(f(U), $product(-1, U)), 0)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq(f(U), U)) <=> ![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq(f(U), U)) <=> ![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.38 inference(or_elim,[status(thm)],[7])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.20/0.38 tff(28,plain,(
% 0.20/0.38 ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.38 inference(skolemize,[status(sab)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0))) <=> ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~$greatereq($sum($sum(W!0, f(V!1)), $product(-1, f($sum(W!0, f(V!1))))), 0)) <=> (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum($sum(W!0, f(V!1)), $product(-1, f($sum(W!0, f(V!1))))), 0))) <=> ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum($sum(W!0, f(V!1)), $product(-1, f($sum(W!0, f(V!1))))), 0))) <=> ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum($sum(W!0, f(V!1)), $product(-1, f($sum(W!0, f(V!1))))), 0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (~$greatereq($sum(W!0, $sum(f(V!1), $product(-1, f($sum(W!0, f(V!1)))))), 0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[35, 29])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(V!1, $product(-1, f(V!1))), 0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (~$greatereq($sum(V!1, $product(-1, f(V!1))), 0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[37, 29])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(theory_lemma,[status(thm)],[38, 36, 16])).
% 0.20/0.38 % SZS output end Proof
%------------------------------------------------------------------------------