TSTP Solution File: NUM857+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM857+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:12:19 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM857+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 15:35:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(vmul_type, type, (
% 0.19/0.41 vmul: ( $i * $i ) > $i)).
% 0.19/0.41 tff(vd530_type, type, (
% 0.19/0.41 vd530: $i)).
% 0.19/0.41 tff(vd527_type, type, (
% 0.19/0.41 vd527: $i)).
% 0.19/0.41 tff(vd529_type, type, (
% 0.19/0.41 vd529: $i)).
% 0.19/0.41 tff(vd526_type, type, (
% 0.19/0.41 vd526: $i)).
% 0.19/0.41 tff(greater_type, type, (
% 0.19/0.41 greater: ( $i * $i ) > $o)).
% 0.19/0.41 tff(geq_type, type, (
% 0.19/0.41 geq: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[Vd244: $i, Vd245: $i] : refl((geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[Vd244: $i, Vd245: $i] : rewrite((geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,axiom,(![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 16), 1)'')).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (geq(vd529, vd530) <=> geq(vd529, vd530)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(14,axiom,(geq(vd529, vd530)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct2(antec(323)), 531, 0)'')).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (geq(vd529, vd530)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 ((~(geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))) | (~geq(vd529, vd530)) | ((vd529 = vd530) | greater(vd529, vd530))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~(geq(vd529, vd530) <=> ((vd529 = vd530) | greater(vd529, vd530)))) | ((vd529 = vd530) | greater(vd529, vd530))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((vd529 = vd530) | greater(vd529, vd530)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[17, 12])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (geq(vmul(vd526, vd529), vmul(vd527, vd530)) <=> ((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[19, 10])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 ((~geq(vmul(vd526, vd529), vmul(vd527, vd530))) <=> (~geq(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(~geq(vmul(vd526, vd529), vmul(vd527, vd530))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conseq(323), 532, 0)'')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (~geq(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~(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))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~(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))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[25, 20])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))) | (~greater(vmul(vd526, vd529), vmul(vd527, vd530)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (~greater(vmul(vd526, vd529), vmul(vd527, vd530))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.41 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/sandbox2/benchmark/theBenchmark.p',''ass(cond(318, 0), 0)'')).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.41 tff(39,plain,(
% 0.19/0.41 ![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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![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)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 41, 28])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527))))) | ((~greater(vd529, vd530)) | (~geq(vd526, vd527)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~greater(vd529, vd530)) | (~geq(vd526, vd527))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (geq(vd526, vd527) <=> geq(vd526, vd527)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(49,axiom,(geq(vd526, vd527)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conjunct1(antec(323)), 528, 0)'')).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (geq(vd526, vd527)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))) | (~greater(vd529, vd530)) | (~geq(vd526, vd527))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((~((~greater(vd529, vd530)) | (~geq(vd526, vd527)))) | (~greater(vd529, vd530))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (~greater(vd529, vd530)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~((vd529 = vd530) | greater(vd529, vd530))) | (vd529 = vd530) | greater(vd529, vd530)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (vd529 = vd530),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[54, 53, 18])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~(geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))) | (~geq(vd526, vd527)) | ((vd526 = vd527) | greater(vd526, vd527))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~(geq(vd526, vd527) <=> ((vd526 = vd527) | greater(vd526, vd527)))) | ((vd526 = vd527) | greater(vd526, vd527))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 50])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((vd526 = vd527) | greater(vd526, vd527)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[59, 57])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~((~greater(vd529, vd530)) | (~geq(vd526, vd527))))) | ((~geq(vd529, vd530)) | (~greater(vd526, vd527)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((~geq(vd529, vd530)) | (~greater(vd526, vd527))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 45])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~geq(vd529, vd530)) | (~greater(vd526, vd527))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~((~geq(vd529, vd530)) | (~greater(vd526, vd527)))) | (~greater(vd526, vd527))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[63, 15])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (~greater(vd526, vd527)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 ((~((vd526 = vd527) | greater(vd526, vd527))) | (vd526 = vd527) | greater(vd526, vd527)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (vd526 = vd527),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[66, 65, 60])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (vmul(vd526, vd529) = vmul(vd527, vd530)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[67, 55])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (((vmul(vd526, vd529) = vmul(vd527, vd530)) | greater(vmul(vd526, vd529), vmul(vd527, vd530))) | (~(vmul(vd526, vd529) = vmul(vd527, vd530)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (~(vmul(vd526, vd529) = vmul(vd527, vd530))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[69, 26])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[70, 68])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------