TSTP Solution File: NUM839+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM839+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 13:12:11 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM839+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 15:41:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(less_type, type, (
% 0.19/0.39 less: ( $i * $i ) > $o)).
% 0.19/0.39 tff(vplus_type, type, (
% 0.19/0.39 vplus: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vd330_type, type, (
% 0.19/0.39 vd330: $i)).
% 0.19/0.39 tff(vd329_type, type, (
% 0.19/0.39 vd329: $i)).
% 0.19/0.39 tff(vd328_type, type, (
% 0.19/0.39 vd328: $i)).
% 0.19/0.39 tff(greater_type, type, (
% 0.19/0.39 greater: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[Vd203: $i, Vd204: $i] : refl(((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 2)'')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (greater(vplus(vd328, vd330), vplus(vd329, vd330)) <=> greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,axiom,(greater(vplus(vd328, vd330), vplus(vd329, vd330))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(antec(204), 331, 0)'')).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (((~![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (^[Vd203: $i, Vd204: $i] : refl(((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,axiom,(![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 3)'')).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,(
% 0.19/0.39 ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | ((~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | (~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | ((~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | (~(vplus(vd328, vd330) = vplus(vd329, vd330))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~(vplus(vd328, vd330) = vplus(vd329, vd330))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[24, 10, 21])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite(((Vd301 = Vd302) => (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))) <=> ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.39 tff(31,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : ((Vd301 = Vd302) => (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 1)'')).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.39 tff(34,plain,(
% 0.19/0.39 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (((~![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | ((~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~(Vd301 = Vd302)) | (vplus(Vd301, Vd303) = vplus(Vd302, Vd303)))) | (~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~(vd328 = vd329)) | (vplus(vd328, vd330) = vplus(vd329, vd330))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (~(vd328 = vd329)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (^[Vd203: $i, Vd204: $i] : refl((less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,axiom,(![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 0)'')).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.40 tff(49,plain,(
% 0.19/0.40 ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(skolemize,[status(sab)],[48])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 ((~greater(vd328, vd329)) <=> (~greater(vd328, vd329))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,axiom,(~greater(vd328, vd329)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(204), 332, 0)'')).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (~greater(vd328, vd329)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329)) <=> (greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (((~![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))) | (greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (((~![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))) | greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329))),
% 0.19/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | greater(vd328, vd329) | (vd328 = vd329) | less(vd328, vd329)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((vd328 = vd329) | less(vd328, vd329)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[59, 53, 50])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (less(vd328, vd329)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 40])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite((less(Vd301, Vd302) => less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : (less(Vd301, Vd302) => less(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : (less(Vd301, Vd302) => less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 0)'')).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.40 tff(70,plain,(
% 0.19/0.40 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~less(vd328, vd329)) | less(vplus(vd328, vd330), vplus(vd329, vd330)))) <=> ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~less(vd328, vd329)) | less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~less(vd328, vd329)) | less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~less(Vd301, Vd302)) | less(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~less(vd328, vd329)) | less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 71, 61, 14])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------