TSTP Solution File: NUM840+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM840+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 13:12:12 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM840+2 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n007.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 : Fri Sep 2 15:05:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(greater_type, type, (
% 0.18/0.39 greater: ( $i * $i ) > $o)).
% 0.18/0.39 tff(vplus_type, type, (
% 0.18/0.39 vplus: ( $i * $i ) > $i)).
% 0.18/0.39 tff(vd329_type, type, (
% 0.18/0.39 vd329: $i)).
% 0.18/0.39 tff(vd328_type, type, (
% 0.18/0.39 vd328: $i)).
% 0.18/0.39 tff(vd330_type, type, (
% 0.18/0.39 vd330: $i)).
% 0.18/0.39 tff(less_type, type, (
% 0.18/0.39 less: ( $i * $i ) > $o)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite((greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.39 tff(6,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 2)'')).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,(
% 0.18/0.39 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[8])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite(((Vd301 = Vd302) => (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((Vd301 = Vd302) => (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.39 tff(16,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : ((Vd301 = Vd302) => (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 1)'')).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.39 tff(19,plain,(
% 0.18/0.39 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[18])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (^[Vd203: $i, Vd204: $i] : refl(((~(Vd203 = Vd204)) | (~less(Vd203, Vd204))) <=> ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(24,axiom,(![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 1)'')).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.39 tff(26,plain,(
% 0.18/0.39 ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[25])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (less(vplus(vd328, vd330), vplus(vd329, vd330)) <=> less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(29,axiom,(less(vplus(vd328, vd330), vplus(vd329, vd330))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(antec(conjunct2(conjunct2(204))), 335, 0)'')).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))) | ((~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))) | (~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))) | ((~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~less(Vd203, Vd204)))) | (~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (~(vplus(vd328, vd330) = vplus(vd329, vd330))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[33, 30, 27])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | ((~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330)))) <=> ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | (~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | ((~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | (~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (~(vd328 = vd329)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[37, 34, 20])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (^[Vd203: $i, Vd204: $i] : refl((less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.39 tff(44,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)'')).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.39 tff(47,plain,(
% 0.18/0.39 ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(skolemize,[status(sab)],[46])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((~less(vd328, vd329)) <=> (~less(vd328, vd329))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(50,axiom,(~less(vd328, vd329)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conseq(conjunct2(conjunct2(204))), 336, 0)'')).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (~less(vd328, vd329)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329)) <=> (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.18/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 ((vd328 = vd329) | greater(vd328, vd329)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[57, 51, 48])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (greater(vd328, vd329)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[58, 38])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (^[Vd203: $i, Vd204: $i] : refl(((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(63,axiom,(![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 2)'')).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.40 tff(65,plain,(
% 0.18/0.40 ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[64])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (~greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[69, 30, 66])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))) <=> ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[73, 70, 59, 10])).
% 0.18/0.40 % SZS output end Proof
%------------------------------------------------------------------------------