TSTP Solution File: NUM843+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM843+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 13:12:13 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM843+2 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 15:25:14 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(vd391_type, type, (
% 0.20/0.41 vd391: $i)).
% 0.20/0.41 tff(vd390_type, type, (
% 0.20/0.41 vd390: $i)).
% 0.20/0.41 tff(less_type, type, (
% 0.20/0.41 less: ( $i * $i ) > $o)).
% 0.20/0.41 tff(leq_type, type, (
% 0.20/0.41 leq: ( $i * $i ) > $o)).
% 0.20/0.41 tff(greater_type, type, (
% 0.20/0.41 greater: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[Vd249: $i, Vd250: $i] : refl((leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249))) <=> (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249))) <=> ![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249))) <=> ![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[Vd249: $i, Vd250: $i] : rewrite((leq(Vd250, Vd249) <=> (less(Vd250, Vd249) | (Vd250 = Vd249))) <=> (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> (less(Vd250, Vd249) | (Vd250 = Vd249))) <=> ![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,axiom,(![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> (less(Vd250, Vd249) | (Vd250 = Vd249)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 17), 1)'')).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,(
% 0.20/0.41 ![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ((~![Vd249: $i, Vd250: $i] : (leq(Vd250, Vd249) <=> ((Vd250 = Vd249) | less(Vd250, Vd249)))) | (leq(vd390, vd391) <=> ((vd390 = vd391) | less(vd390, vd391)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (leq(vd390, vd391) <=> ((vd390 = vd391) | less(vd390, vd391))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 ((~leq(vd390, vd391)) <=> (~leq(vd390, vd391))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(14,axiom,(~leq(vd390, vd391)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct2(243), 393, 0)'')).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~leq(vd390, vd391)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 ((~(leq(vd390, vd391) <=> ((vd390 = vd391) | less(vd390, vd391)))) | leq(vd390, vd391) | (~((vd390 = vd391) | less(vd390, vd391)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 ((~(leq(vd390, vd391) <=> ((vd390 = vd391) | less(vd390, vd391)))) | (~((vd390 = vd391) | less(vd390, vd391)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~((vd390 = vd391) | less(vd390, vd391))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (((vd390 = vd391) | less(vd390, vd391)) | (~(vd390 = vd391))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~(vd390 = vd391)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (((vd390 = vd391) | less(vd390, vd391)) | (~less(vd390, vd391))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~less(vd390, vd391)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[21, 18])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (^[Vd203: $i, Vd204: $i] : refl((greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204)) <=> (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.41 tff(28,axiom,(![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 0)'')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.41 tff(31,plain,(
% 0.20/0.41 ![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(skolemize,[status(sab)],[30])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~greater(vd390, vd391)) <=> (~greater(vd390, vd391))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,axiom,(~greater(vd390, vd391)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(244, 394, 0)'')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (~greater(vd390, vd391)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391))) <=> ((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((greater(vd390, vd391) | less(vd390, vd391) | (vd390 = vd391)) <=> (greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd390, vd391) | less(vd390, vd391) | (vd390 = vd391))) <=> ((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd390, vd391) | less(vd390, vd391) | (vd390 = vd391))) <=> ((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391))),
% 0.20/0.41 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd390, vd391) | less(vd390, vd391) | (vd390 = vd391))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~![Vd203: $i, Vd204: $i] : (greater(Vd203, Vd204) | less(Vd203, Vd204) | (Vd203 = Vd204))) | greater(vd390, vd391) | (vd390 = vd391) | less(vd390, vd391)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((vd390 = vd391) | less(vd390, vd391)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[41, 35, 32])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 22, 20])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------