%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM855+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:22:14 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM855+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 Jun 20 02:02:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(less_type, type, (
% 0.21/0.39 less: ( $i * $i ) > $o)).
% 0.21/0.39 tff(vmul_type, type, (
% 0.21/0.39 vmul: ( $i * $i ) > $i)).
% 0.21/0.39 tff(vd511_type, type, (
% 0.21/0.39 vd511: $i)).
% 0.21/0.39 tff(vd508_type, type, (
% 0.21/0.39 vd508: $i)).
% 0.21/0.39 tff(vd509_type, type, (
% 0.21/0.39 vd509: $i)).
% 0.21/0.39 tff(greater_type, type, (
% 0.21/0.39 greater: ( $i * $i ) > $o)).
% 0.21/0.39 tff(vd512_type, type, (
% 0.21/0.39 vd512: $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((vmul(vd509, vd511) = vmul(vd511, vd509)) <=> (vmul(vd509, vd511) = vmul(vd511, vd509))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,axiom,(vmul(vd509, vd511) = vmul(vd511, vd509)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct2(315), 515, 0)'')).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (vmul(vd509, vd511) = vmul(vd511, vd509)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (vmul(vd511, vd509) = vmul(vd509, vd511)),
% 0.21/0.39 inference(symmetry,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (less(vmul(vd511, vd509), vmul(vd508, vd511)) <=> less(vmul(vd509, vd511), vmul(vd508, vd511))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (less(vmul(vd509, vd511), vmul(vd508, vd511)) <=> less(vmul(vd511, vd509), vmul(vd508, vd511))),
% 0.21/0.39 inference(symmetry,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (^[Vd208: $i, Vd209: $i] : refl(((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (^[Vd208: $i, Vd209: $i] : rewrite((greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,axiom,(![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(140, 0), 0)'')).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (greater(vd508, vd509) <=> greater(vd508, vd509)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(18,axiom,(greater(vd508, vd509)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct1(314), 510, 0)'')).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (greater(vd508, vd509)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vd508, vd509)) | less(vd509, vd508))) <=> ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vd508, vd509)) | less(vd509, vd508))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vd508, vd509)) | less(vd509, vd508))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vd508, vd509)) | less(vd509, vd508)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (less(vd509, vd508)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[22, 19, 16])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (^[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))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.40 tff(29,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)'')).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.40 tff(32,plain,(
% 0.21/0.40 ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[31])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd509, vd508)) | less(vmul(vd509, vd511), vmul(vd508, vd511)))) <=> ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd509, vd508)) | less(vmul(vd509, vd511), vmul(vd508, vd511)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd509, vd508)) | less(vmul(vd509, vd511), vmul(vd508, vd511)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(36,plain,
% 0.21/0.40 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd509, vd508)) | less(vmul(vd509, vd511), vmul(vd508, vd511))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((~less(vd509, vd508)) | less(vmul(vd509, vd511), vmul(vd508, vd511))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (less(vmul(vd509, vd511), vmul(vd508, vd511))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[37, 23])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (less(vmul(vd511, vd509), vmul(vd508, vd511))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[38, 6])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((vmul(vd512, vd509) = vmul(vd509, vd512)) <=> (vmul(vd512, vd509) = vmul(vd509, vd512))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(41,axiom,(vmul(vd512, vd509) = vmul(vd509, vd512)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct2(315), 515, 2)'')).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (vmul(vd512, vd509) = vmul(vd509, vd512)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (vmul(vd509, vd512) = vmul(vd512, vd509)),
% 0.21/0.40 inference(symmetry,[status(thm)],[42])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (less(vmul(vd509, vd512), vmul(vd511, vd509)) <=> less(vmul(vd512, vd509), vmul(vd511, vd509))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (less(vmul(vd512, vd509), vmul(vd511, vd509)) <=> less(vmul(vd509, vd512), vmul(vd511, vd509))),
% 0.21/0.40 inference(symmetry,[status(thm)],[44])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (greater(vd511, vd512) <=> greater(vd511, vd512)),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(47,axiom,(greater(vd511, vd512)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct2(314), 513, 0)'')).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (greater(vd511, vd512)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vd511, vd512)) | less(vd512, vd511))) <=> ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vd511, vd512)) | less(vd512, vd511))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vd511, vd512)) | less(vd512, vd511))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vd511, vd512)) | less(vd512, vd511)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (less(vd512, vd511)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 48, 16])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd512, vd511)) | less(vmul(vd512, vd509), vmul(vd511, vd509)))) <=> ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd512, vd511)) | less(vmul(vd512, vd509), vmul(vd511, vd509)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | ((~less(vd512, vd511)) | less(vmul(vd512, vd509), vmul(vd511, vd509)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))) | (~less(vd512, vd511)) | less(vmul(vd512, vd509), vmul(vd511, vd509))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ((~less(vd512, vd511)) | less(vmul(vd512, vd509), vmul(vd511, vd509))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 33])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (less(vmul(vd512, vd509), vmul(vd511, vd509))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[56, 52])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (less(vmul(vd509, vd512), vmul(vd511, vd509))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[57, 45])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (^[Vd226: $i, Vd227: $i] : refl(((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (^[Vd226: $i, Vd227: $i] : rewrite((less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.40 tff(64,axiom,(![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(147, 0), 0)'')).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.40 tff(67,plain,(
% 0.21/0.40 ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(skolemize,[status(sab)],[66])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 ((~greater(vmul(vd508, vd511), vmul(vd509, vd512))) <=> (~greater(vmul(vd508, vd511), vmul(vd509, vd512)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,axiom,(~greater(vmul(vd508, vd511), vmul(vd509, vd512))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq_conjunct2(315), 516, 0)'')).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (~greater(vmul(vd508, vd511), vmul(vd509, vd512))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vmul(vd509, vd512), vmul(vd508, vd511))) | greater(vmul(vd508, vd511), vmul(vd509, vd512)))) <=> ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vmul(vd509, vd512), vmul(vd508, vd511))) | greater(vmul(vd508, vd511), vmul(vd509, vd512)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vmul(vd509, vd512), vmul(vd508, vd511))) | greater(vmul(vd508, vd511), vmul(vd509, vd512)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vmul(vd509, vd512), vmul(vd508, vd511))) | greater(vmul(vd508, vd511), vmul(vd509, vd512))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (~less(vmul(vd509, vd512), vmul(vd508, vd511))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 71, 68])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (^[Vd262: $i, Vd263: $i, Vd265: $i] : trans(monotonicity(trans(monotonicity(rewrite((less(Vd263, Vd265) & less(Vd262, Vd263)) <=> (~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))), ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) <=> (~(~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))))), rewrite((~(~((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))) <=> ((~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))), ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) <=> ((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))))), (((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) | less(Vd262, Vd265)))), rewrite((((~less(Vd263, Vd265)) | (~less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))), (((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (^[Vd262: $i, Vd263: $i, Vd265: $i] : rewrite(((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265)) <=> ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265)) <=> ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.40 tff(82,axiom,(![Vd262: $i, Vd263: $i, Vd265: $i] : ((less(Vd263, Vd265) & less(Vd262, Vd263)) => less(Vd262, Vd265))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(168, 0), 0)'')).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.21/0.40 tff(85,plain,(
% 0.21/0.40 ![Vd262: $i, Vd263: $i, Vd265: $i] : ((~(less(Vd263, Vd265) & less(Vd262, Vd263))) | less(Vd262, Vd265))),
% 0.21/0.40 inference(skolemize,[status(sab)],[84])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(89,plain,
% 0.21/0.40 ((less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))) | (~less(vmul(vd509, vd512), vmul(vd511, vd509)))) <=> (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))))) <=> ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | (less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd511, vd509), vmul(vd508, vd511))) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 ((~![Vd262: $i, Vd263: $i, Vd265: $i] : (less(Vd262, Vd265) | (~less(Vd263, Vd265)) | (~less(Vd262, Vd263)))) | less(vmul(vd509, vd512), vmul(vd508, vd511)) | (~less(vmul(vd509, vd512), vmul(vd511, vd509))) | (~less(vmul(vd511, vd509), vmul(vd508, vd511)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 87, 75, 58, 39])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------