TSTP Solution File: NUM853+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM853+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM853+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n020.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 15:26:29 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(less_type, type, (
% 0.12/0.40 less: ( $i * $i ) > $o)).
% 0.12/0.40 tff(vmul_type, type, (
% 0.12/0.40 vmul: ( $i * $i ) > $i)).
% 0.12/0.40 tff(vd487_type, type, (
% 0.12/0.40 vd487: $i)).
% 0.12/0.40 tff(vd488_type, type, (
% 0.12/0.40 vd488: $i)).
% 0.12/0.40 tff(vd486_type, type, (
% 0.12/0.40 vd486: $i)).
% 0.12/0.40 tff(greater_type, type, (
% 0.12/0.40 greater: ( $i * $i ) > $o)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (^[Vd203: $i, Vd204: $i] : refl(((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 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)'')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,(
% 0.12/0.40 ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[5])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (greater(vmul(vd486, vd487), vmul(vd488, vd487)) <=> greater(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,axiom,(greater(vmul(vd486, vd487), vmul(vd488, vd487))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(antec(307), 489, 0)'')).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (greater(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (~less(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (^[Vd203: $i, Vd204: $i] : refl(((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 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)'')).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.40 tff(20,plain,(
% 0.12/0.40 ![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[19])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | ((~(vmul(vd486, vd487) = vmul(vd488, vd487))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | (~(vmul(vd486, vd487) = vmul(vd488, vd487))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | ((~(vmul(vd486, vd487) = vmul(vd488, vd487))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 ((~![Vd203: $i, Vd204: $i] : ((~(Vd203 = Vd204)) | (~greater(Vd203, Vd204)))) | (~(vmul(vd486, vd487) = vmul(vd488, vd487))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 (~(vmul(vd486, vd487) = vmul(vd488, vd487))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[24, 10, 21])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (^[Vd456: $i, Vd461: $i, Vd462: $i] : refl(((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))) <=> ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))) <=> ![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))) <=> ![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (^[Vd456: $i, Vd461: $i, Vd462: $i] : rewrite(((Vd461 = Vd462) => (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))) <=> ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((Vd461 = Vd462) => (vmul(Vd461, Vd456) = vmul(Vd462, Vd456))) <=> ![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.41 tff(31,axiom,(![Vd456: $i, Vd461: $i, Vd462: $i] : ((Vd461 = Vd462) => (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(299, 0), 1)'')).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.41 tff(34,plain,(
% 0.12/0.41 ![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[33])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 (![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (((~![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))) | ((~(vd486 = vd488)) | (vmul(vd486, vd487) = vmul(vd488, vd487)))) <=> ((~![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))) | (~(vd486 = vd488)) | (vmul(vd486, vd487) = vmul(vd488, vd487)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 ((~![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))) | ((~(vd486 = vd488)) | (vmul(vd486, vd487) = vmul(vd488, vd487)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 ((~![Vd456: $i, Vd461: $i, Vd462: $i] : ((~(Vd461 = Vd462)) | (vmul(Vd461, Vd456) = vmul(Vd462, Vd456)))) | (~(vd486 = vd488)) | (vmul(vd486, vd487) = vmul(vd488, vd487))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 ((~(vd486 = vd488)) | (vmul(vd486, vd487) = vmul(vd488, vd487))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (~(vd486 = vd488)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (^[Vd203: $i, Vd204: $i] : refl((less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.41 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)'')).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.12/0.41 tff(49,plain,(
% 0.12/0.41 ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(skolemize,[status(sab)],[48])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 ((~greater(vd486, vd488)) <=> (~greater(vd486, vd488))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(52,axiom,(~greater(vd486, vd488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(307), 490, 0)'')).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (~greater(vd486, vd488)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 ((less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488)) <=> (greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[55])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488))),
% 0.12/0.41 inference(transitivity,[status(thm)],[56, 54])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | greater(vd486, vd488) | (vd486 = vd488) | less(vd486, vd488)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 ((vd486 = vd488) | less(vd486, vd488)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[59, 53, 50])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (less(vd486, vd488)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[60, 40])).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (^[Vd456: $i, Vd465: $i, Vd466: $i] : refl(((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))) <=> ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))) <=> ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))) <=> ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (^[Vd456: $i, Vd465: $i, Vd466: $i] : rewrite((less(Vd465, Vd466) => less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))) <=> ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : (less(Vd465, Vd466) => less(vmul(Vd465, Vd456), vmul(Vd466, Vd456))) <=> ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.41 tff(67,axiom,(![Vd456: $i, Vd465: $i, Vd466: $i] : (less(Vd465, Vd466) => less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(299, 0), 0)'')).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.12/0.41 tff(70,plain,(
% 0.12/0.41 ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[69])).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 (((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd486, vd488)) | less(vmul(vd486, vd487), vmul(vd488, vd487)))) <=> ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd486, vd488)) | less(vmul(vd486, vd487), vmul(vd488, vd487)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd486, vd488)) | less(vmul(vd486, vd487), vmul(vd488, vd487)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd486, vd488)) | less(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[74, 71, 61, 14])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------