%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM853+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : NUM853+2 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:01:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(less_type, type, (
% 0.18/0.36 less: ( $i * $i ) > $o)).
% 0.18/0.36 tff(vmul_type, type, (
% 0.18/0.36 vmul: ( $i * $i ) > $i)).
% 0.18/0.36 tff(vd487_type, type, (
% 0.18/0.36 vd487: $i)).
% 0.18/0.36 tff(vd486_type, type, (
% 0.18/0.36 vd486: $i)).
% 0.18/0.36 tff(vd488_type, type, (
% 0.18/0.36 vd488: $i)).
% 0.18/0.36 tff(greater_type, type, (
% 0.18/0.36 greater: ( $i * $i ) > $o)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (^[Vd203: $i, Vd204: $i] : refl(((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 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)'')).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.36 tff(6,plain,(
% 0.18/0.36 ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[5])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 (greater(vmul(vd486, vd487), vmul(vd488, vd487)) <=> greater(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(9,axiom,(greater(vmul(vd486, vd487), vmul(vd488, vd487))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(antec(307), 489, 0)'')).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (greater(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (((~![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))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | (~less(vmul(vd486, vd487), vmul(vd488, vd487)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (~less(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 (^[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))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (![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)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (![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)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.37 tff(20,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)'')).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.18/0.37 tff(23,plain,(
% 0.18/0.37 ![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[22])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![Vd456: $i, Vd465: $i, Vd466: $i] : ((~less(Vd465, Vd466)) | less(vmul(Vd465, Vd456), vmul(Vd466, Vd456)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (((~![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 ((~![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)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ((~![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))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 ((~less(vd486, vd488)) | less(vmul(vd486, vd487), vmul(vd488, vd487))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (~less(vd486, vd488)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (^[Vd203: $i, Vd204: $i] : refl((less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,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)'')).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.37 tff(38,plain,(
% 0.18/0.37 ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(skolemize,[status(sab)],[37])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 ((~greater(vd486, vd488)) <=> (~greater(vd486, vd488))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(41,axiom,(~greater(vd486, vd488)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(307), 490, 0)'')).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 (~greater(vd486, vd488)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (greater(vd486, vd488) | less(vd486, vd488) | (vd486 = vd488))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | greater(vd486, vd488) | less(vd486, vd488) | (vd486 = vd488))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 ((less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488)) <=> (greater(vd486, vd488) | less(vd486, vd488) | (vd486 = vd488))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (((~![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) | less(vd486, vd488) | (vd486 = vd488)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (((~![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) | less(vd486, vd488) | (vd486 = vd488))),
% 0.18/0.37 inference(transitivity,[status(thm)],[45, 43])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | (less(vd486, vd488) | (vd486 = vd488) | greater(vd486, vd488))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | (Vd203 = Vd204) | greater(Vd203, Vd204))) | greater(vd486, vd488) | less(vd486, vd488) | (vd486 = vd488)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (less(vd486, vd488) | (vd486 = vd488)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[48, 42, 39])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (vd486 = vd488),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[49, 29])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (vd488 = vd486),
% 0.18/0.37 inference(symmetry,[status(thm)],[50])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (vmul(vd488, vd487) = vmul(vd486, vd487)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[51])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (less(vmul(vd488, vd487), vmul(vd486, vd487)) <=> less(vmul(vd486, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 (less(vmul(vd486, vd487), vmul(vd486, vd487)) <=> less(vmul(vd488, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(symmetry,[status(thm)],[53])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 ((~less(vmul(vd486, vd487), vmul(vd486, vd487))) <=> (~less(vmul(vd488, vd487), vmul(vd486, vd487)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (less(vmul(vd486, vd487), vmul(vd488, vd487)) <=> less(vmul(vd486, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[52])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 ((~less(vmul(vd486, vd487), vmul(vd488, vd487))) <=> (~less(vmul(vd486, vd487), vmul(vd486, vd487)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[56])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (~less(vmul(vd486, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 57])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (~less(vmul(vd488, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (^[Vd208: $i, Vd209: $i] : refl(((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (^[Vd208: $i, Vd209: $i] : rewrite((greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ((~greater(Vd208, Vd209)) | less(Vd209, Vd208)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208)) <=> ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.37 tff(65,axiom,(![Vd208: $i, Vd209: $i] : (greater(Vd208, Vd209) => less(Vd209, Vd208))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(140, 0), 0)'')).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.18/0.37 tff(68,plain,(
% 0.18/0.37 ![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(skolemize,[status(sab)],[67])).
% 0.18/0.37 tff(69,plain,
% 0.18/0.37 (![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 (((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | less(vmul(vd488, vd487), vmul(vd486, vd487)))) <=> ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | less(vmul(vd488, vd487), vmul(vd486, vd487)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | ((~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | less(vmul(vd488, vd487), vmul(vd486, vd487)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 ((~![Vd208: $i, Vd209: $i] : ((~greater(Vd208, Vd209)) | less(Vd209, Vd208))) | (~greater(vmul(vd486, vd487), vmul(vd488, vd487))) | less(vmul(vd488, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 (less(vmul(vd488, vd487), vmul(vd486, vd487))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[72, 10, 69])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------