TSTP Solution File: NUM854+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM854+1 : TPTP v8.1.0. Released v4.1.0.
% 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 13:12:17 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM854+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 15:25:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(greater_type, type, (
% 0.19/0.41 greater: ( $i * $i ) > $o)).
% 0.19/0.41 tff(vmul_type, type, (
% 0.19/0.41 vmul: ( $i * $i ) > $i)).
% 0.19/0.41 tff(vd509_type, type, (
% 0.19/0.41 vd509: $i)).
% 0.19/0.41 tff(vd508_type, type, (
% 0.19/0.41 vd508: $i)).
% 0.19/0.41 tff(vd511_type, type, (
% 0.19/0.41 vd511: $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[Vd456: $i, Vd457: $i, Vd458: $i] : refl(((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[Vd456: $i, Vd457: $i, Vd458: $i] : rewrite((greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,axiom,(![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(299, 0), 2)'')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (greater(vd508, vd509) <=> greater(vd508, vd509)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,axiom,(greater(vd508, vd509)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct1(314), 510, 0)'')).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (greater(vd508, vd509)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~greater(vmul(vd508, vd511), vmul(vd509, vd511))) <=> (~greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,axiom,(~greater(vmul(vd508, vd511), vmul(vd509, vd511))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct1(315), 514, 0)'')).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (~greater(vmul(vd508, vd511), vmul(vd509, vd511))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))) <=> ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 16, 13, 10])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------