TSTP Solution File: NUM921_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM921_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Sun Sep 18 13:12:35 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
% 0.03/0.12 % Problem : NUM921_1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 : Fri Sep 2 15:36:24 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.
% 0.20/0.39 % 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_V_0_type, type, (
% 0.20/0.39 tptp_fun_V_0: $int)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 ((~(~$greatereq($sum(V!0, $product(-1, f(V!0))), 0))) <=> $greatereq($sum(V!0, $product(-1, f(V!0))), 0)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0))) <=> (~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 ((~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))) <=> (~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))) <=> (~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ((~(![U: $int] : $greater(f(U), U) => ![V: $int] : $less($difference(V, f(V)), 0))) <=> (~((~![U: $int] : (~$lesseq(f(U), U))) | ![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,axiom,(~(![U: $int] : $greater(f(U), U) => ![V: $int] : $less($difference(V, f(V)), 0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~((~![U: $int] : (~$lesseq(f(U), U))) | ![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))),
% 0.20/0.39 inference(or_elim,[status(thm)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~![V: $int] : (~$lesseq(0, $sum(V, $product(-1, f(V)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![V: $int] : (~$greatereq($sum(V, $product(-1, f(V))), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.39 tff(15,plain,(
% 0.20/0.39 ~(~$greatereq($sum(V!0, $product(-1, f(V!0))), 0))),
% 0.20/0.39 inference(skolemize,[status(sab)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ($greatereq($sum(V!0, $product(-1, f(V!0))), 0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (^[U: $int] : refl((~$greatereq($sum(U, $product(-1, f(U))), 0)) <=> (~$greatereq($sum(U, $product(-1, f(U))), 0)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0)) <=> ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (^[U: $int] : rewrite((~$lesseq($sum(f(U), $product(-1, U)), 0)) <=> (~$greatereq($sum(U, $product(-1, f(U))), 0)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0)) <=> ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (^[U: $int] : rewrite((~$lesseq(f(U), U)) <=> (~$lesseq($sum(f(U), $product(-1, U)), 0)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq(f(U), U)) <=> ![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq(f(U), U)) <=> ![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.39 inference(or_elim,[status(thm)],[7])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq(f(U), U))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![U: $int] : (~$lesseq($sum(f(U), $product(-1, U)), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.20/0.39 tff(28,plain,(
% 0.20/0.39 ![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.39 inference(skolemize,[status(sab)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![U: $int] : (~$greatereq($sum(U, $product(-1, f(U))), 0))) | (~$greatereq($sum(V!0, $product(-1, f(V!0))), 0))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29, 16])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------