%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM856+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:22:15 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM856+2 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 02:06:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(greater_type, type, (
% 0.13/0.40 greater: ( $i * $i ) > $o)).
% 0.13/0.40 tff(vmul_type, type, (
% 0.13/0.40 vmul: ( $i * $i ) > $i)).
% 0.13/0.40 tff(vd518_type, type, (
% 0.13/0.40 vd518: $i)).
% 0.13/0.40 tff(vd520_type, type, (
% 0.13/0.40 vd520: $i)).
% 0.13/0.40 tff(vd519_type, type, (
% 0.13/0.40 vd519: $i)).
% 0.13/0.40 tff(vd517_type, type, (
% 0.13/0.40 vd517: $i)).
% 0.13/0.40 tff(geq_type, type, (
% 0.13/0.40 geq: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[Vd418: $i, Vd419: $i] : refl((vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(270, 0), 0)'')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))) | (vmul(vd520, vd518) = vmul(vd518, vd520))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (vmul(vd520, vd518) = vmul(vd518, vd520)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))) | (vmul(vd519, vd517) = vmul(vd517, vd519))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (vmul(vd519, vd517) = vmul(vd517, vd519)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (^[Vd244: $i, Vd245: $i] : refl((geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (^[Vd244: $i, Vd245: $i] : rewrite((geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.40 tff(17,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)'')).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40 tff(20,plain,(
% 0.13/0.40 ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.13/0.40 tff(26,assumption,(~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))), introduced(assumption)).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (((~geq(vd519, vd520)) | (~greater(vd517, vd518))) | geq(vd519, vd520)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (geq(vd519, vd520)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((~(geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))) | (~geq(vd519, vd520)) | ((vd519 = vd520) | greater(vd519, vd520))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((~(geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))) | ((vd519 = vd520) | greater(vd519, vd520))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((vd519 = vd520) | greater(vd519, vd520)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[30, 25])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (((~geq(vd519, vd520)) | (~greater(vd517, vd518))) | greater(vd517, vd518)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (greater(vd517, vd518)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[32, 26])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (^[Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : refl((greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))) <=> (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))) <=> ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (^[Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(Vd504, Vd505) & greater(Vd501, Vd502)) <=> (~((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))))), ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) <=> (~(~((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))))))), rewrite((~(~((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))))) <=> ((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))), ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) <=> ((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))))), (((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> (((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))))), rewrite((((~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))), (((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (^[Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : rewrite(((greater(Vd504, Vd505) & greater(Vd501, Vd502)) => greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((greater(Vd504, Vd505) & greater(Vd501, Vd502)) => greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505))) <=> ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.40 tff(41,axiom,(![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((greater(Vd504, Vd505) & greater(Vd501, Vd502)) => greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(312, 0), 0)'')).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.40 tff(44,plain,(
% 0.13/0.40 ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 ((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) <=> (~greater(vmul(vd517, vd519), vmul(vd518, vd520)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,axiom,(~greater(vmul(vd517, vd519), vmul(vd518, vd520))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(scope(318)), 525, 0)'')).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (~greater(vmul(vd517, vd519), vmul(vd518, vd520))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (((~![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))) | (greater(vmul(vd517, vd519), vmul(vd518, vd520)) | (~greater(vd519, vd520)) | (~greater(vd517, vd518)))) <=> ((~![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))) | greater(vmul(vd517, vd519), vmul(vd518, vd520)) | (~greater(vd519, vd520)) | (~greater(vd517, vd518)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))) | (greater(vmul(vd517, vd519), vmul(vd518, vd520)) | (~greater(vd519, vd520)) | (~greater(vd517, vd518)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 ((~![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))) | greater(vmul(vd517, vd519), vmul(vd518, vd520)) | (~greater(vd519, vd520)) | (~greater(vd517, vd518))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 ((~greater(vd519, vd520)) | (~greater(vd517, vd518))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[52, 49, 46])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (~greater(vd519, vd520)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[53, 33])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~((vd519 = vd520) | greater(vd519, vd520))) | (vd519 = vd520) | greater(vd519, vd520)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 ((~((vd519 = vd520) | greater(vd519, vd520))) | (vd519 = vd520)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (vd519 = vd520),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[56, 31])).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 (vd520 = vd519),
% 0.13/0.40 inference(symmetry,[status(thm)],[57])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (vmul(vd517, vd520) = vmul(vd517, vd519)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (greater(vmul(vd517, vd520), vmul(vd518, vd520)) <=> greater(vmul(vd517, vd519), vmul(vd518, vd520))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (greater(vmul(vd517, vd519), vmul(vd518, vd520)) <=> greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.21/0.40 inference(symmetry,[status(thm)],[60])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 ((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) <=> (~greater(vmul(vd517, vd520), vmul(vd518, vd520)))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (~greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[49, 62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (^[Vd456: $i, Vd457: $i, Vd458: $i] : refl(((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (^[Vd456: $i, Vd457: $i, Vd458: $i] : rewrite((greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.40 tff(69,axiom,(![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(299, 0), 2)'')).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.40 tff(72,plain,(
% 0.21/0.40 ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[71])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 (((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd517, vd518)) | greater(vmul(vd517, vd520), vmul(vd518, vd520)))) <=> ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd517, vd518)) | greater(vmul(vd517, vd520), vmul(vd518, vd520)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd517, vd518)) | greater(vmul(vd517, vd520), vmul(vd518, vd520)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd517, vd518)) | greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 33, 73])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[77, 63])).
% 0.21/0.41 tff(79,plain,((~geq(vd519, vd520)) | (~greater(vd517, vd518))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 (((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((geq(vd519, vd520) & greater(vd517, vd518)) <=> (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) <=> (~((~greater(vd519, vd520)) | (~geq(vd517, vd518))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[82, 81])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[83, 80])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(86,axiom,((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''dis(antec(scope(318)))'')).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[87, 85])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[88, 85])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[90, 85])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[92, 79])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (((~greater(vd519, vd520)) | (~geq(vd517, vd518))) | geq(vd517, vd518)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (geq(vd517, vd518)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((~(geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))) | (~geq(vd517, vd518)) | ((vd517 = vd518) | greater(vd517, vd518))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 ((~(geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))) | ((vd517 = vd518) | greater(vd517, vd518))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((vd517 = vd518) | greater(vd517, vd518)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[97, 23])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (((~greater(vd519, vd520)) | (~geq(vd517, vd518))) | greater(vd519, vd520)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (greater(vd519, vd520)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 93])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (~greater(vd517, vd518)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 100])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 ((~((vd517 = vd518) | greater(vd517, vd518))) | (vd517 = vd518) | greater(vd517, vd518)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 ((~((vd517 = vd518) | greater(vd517, vd518))) | (vd517 = vd518)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (vd517 = vd518),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[103, 98])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (vd518 = vd517),
% 0.21/0.41 inference(symmetry,[status(thm)],[104])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (vmul(vd519, vd518) = vmul(vd519, vd517)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (vmul(vd519, vd518) = vmul(vd517, vd519)),
% 0.21/0.41 inference(transitivity,[status(thm)],[106, 11])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (greater(vmul(vd519, vd518), vmul(vd520, vd518)) <=> greater(vmul(vd517, vd519), vmul(vd518, vd520))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[107, 9])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (greater(vmul(vd517, vd519), vmul(vd518, vd520)) <=> greater(vmul(vd519, vd518), vmul(vd520, vd518))),
% 0.21/0.41 inference(symmetry,[status(thm)],[108])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 ((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) <=> (~greater(vmul(vd519, vd518), vmul(vd520, vd518)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[109])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (~greater(vmul(vd519, vd518), vmul(vd520, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 110])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd519, vd520)) | greater(vmul(vd519, vd518), vmul(vd520, vd518)))) <=> ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd519, vd520)) | greater(vmul(vd519, vd518), vmul(vd520, vd518)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd519, vd520)) | greater(vmul(vd519, vd518), vmul(vd520, vd518)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd519, vd520)) | greater(vmul(vd519, vd518), vmul(vd520, vd518))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 (greater(vmul(vd519, vd518), vmul(vd520, vd518))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[114, 100, 73])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[115, 111])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------