%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM857+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:22:15 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM857+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 02:04:01 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(vmul_type, type, (
% 0.20/0.38 vmul: ( $i * $i ) > $i)).
% 0.20/0.38 tff(vd530_type, type, (
% 0.20/0.38 vd530: $i)).
% 0.20/0.38 tff(vd527_type, type, (
% 0.20/0.38 vd527: $i)).
% 0.20/0.38 tff(vd529_type, type, (
% 0.20/0.38 vd529: $i)).
% 0.20/0.38 tff(vd526_type, type, (
% 0.20/0.38 vd526: $i)).
% 0.20/0.38 tff(greater_type, type, (
% 0.20/0.38 greater: ( $i * $i ) > $o)).
% 0.20/0.38 tff(geq_type, type, (
% 0.20/0.38 geq: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[Vd244: $i, Vd245: $i] : refl((geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[Vd244: $i, Vd245: $i] : rewrite((geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,axiom,(![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 16), 1)'')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,(
% 0.20/0.38 ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (geq(vd529, vd530) <=> geq(vd529, vd530)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,axiom,(geq(vd529, vd530)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct2(antec(323)), 531, 0)'')).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (geq(vd529, vd530)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((~(geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))) | (~geq(vd529, vd530)) | ((vd529 = vd530) | greater(vd529, vd530))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~(geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))) | ((vd529 = vd530) | greater(vd529, vd530))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((vd529 = vd530) | greater(vd529, vd530)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vmul(vd526, vd529), vmul(vd527, vd530)) <=> ((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (geq(vmul(vd526, vd529), vmul(vd527, vd530)) <=> ((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 10])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~geq(vmul(vd526, vd529), vmul(vd527, vd530))) <=> (~geq(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,axiom,(~geq(vmul(vd526, vd529), vmul(vd527, vd530))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(323), 532, 0)'')).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (~geq(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~(geq(vmul(vd526, vd529), vmul(vd527, vd530)) <=> ((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))))) | geq(vmul(vd526, vd529), vmul(vd527, vd530)) | (~((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~(geq(vmul(vd526, vd529), vmul(vd527, vd530)) <=> ((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))))) | (~((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (~((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 20])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))) | (~greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (~greater(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (^[Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : refl(((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : rewrite(((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (^[Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : trans(monotonicity(rewrite(((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) <=> ((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))), ((((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> (((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))))), rewrite((((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))), ((((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : (((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520))) <=> ![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.39 tff(36,axiom,(![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : (((greater(Vd519, Vd520) & geq(Vd517, Vd518)) | (geq(Vd519, Vd520) & greater(Vd517, Vd518))) => greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(318, 0), 0)'')).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.39 tff(39,plain,(
% 0.20/0.39 ![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((geq(Vd519, Vd520) & greater(Vd517, Vd518)) | (greater(Vd519, Vd520) & geq(Vd517, Vd518)))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (((~![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))) | ((~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))) <=> ((~![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))) | (~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))) | ((~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![Vd517: $i, Vd518: $i, Vd519: $i, Vd520: $i] : ((~((~((~geq(Vd519, Vd520)) | (~greater(Vd517, Vd518)))) | (~((~greater(Vd519, Vd520)) | (~geq(Vd517, Vd518)))))) | greater(vmul(Vd517, Vd519), vmul(Vd518, Vd520)))) | (~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))) | greater(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))) | greater(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 28])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527))))) | ((~greater(vd529, vd530)) | (~geq(vd526, vd527)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~greater(vd529, vd530)) | (~geq(vd526, vd527))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (geq(vd526, vd527) <=> geq(vd526, vd527)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(50,axiom,(geq(vd526, vd527)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct1(antec(323)), 528, 0)'')).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (geq(vd526, vd527)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))) | (~greater(vd529, vd530)) | (~geq(vd526, vd527))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))) | (~greater(vd529, vd530))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (~greater(vd529, vd530)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~((vd529 = vd530) | greater(vd529, vd530))) | (vd529 = vd530) | greater(vd529, vd530)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (vd529 = vd530),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54, 18])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 10])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~(geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))) | (~geq(vd526, vd527)) | ((vd526 = vd527) | greater(vd526, vd527))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((~(geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))) | ((vd526 = vd527) | greater(vd526, vd527))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 51])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((vd526 = vd527) | greater(vd526, vd527)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 58])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527))))) | ((~geq(vd529, vd530)) | (~greater(vd526, vd527)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 ((~geq(vd529, vd530)) | (~greater(vd526, vd527))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 46])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~geq(vd529, vd530)) | (~greater(vd526, vd527))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~greater(vd526, vd527))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 15])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (~greater(vd526, vd527)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 63])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~((vd526 = vd527) | greater(vd526, vd527))) | (vd526 = vd527) | greater(vd526, vd527)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (vd526 = vd527),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 66, 61])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (vmul(vd526, vd529) = vmul(vd527, vd530)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[68, 56])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))) | (~(vmul(vd526, vd529) = vmul(vd527, vd530)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (~(vmul(vd526, vd529) = vmul(vd527, vd530))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[70, 26])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 69])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------