TSTP Solution File: NUM856+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM856+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:12:18 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM856+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 2 15:38:31 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(vplus_type, type, (
% 0.20/0.40 vplus: ( $i * $i ) > $i)).
% 0.20/0.40 tff(vmul_type, type, (
% 0.20/0.40 vmul: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_Vd196_1_type, type, (
% 0.20/0.40 tptp_fun_Vd196_1: ( $i * $i ) > $i)).
% 0.20/0.40 tff(vd520_type, type, (
% 0.20/0.40 vd520: $i)).
% 0.20/0.40 tff(vd519_type, type, (
% 0.20/0.40 vd519: $i)).
% 0.20/0.40 tff(vd518_type, type, (
% 0.20/0.40 vd518: $i)).
% 0.20/0.40 tff(vd517_type, type, (
% 0.20/0.40 vd517: $i)).
% 0.20/0.40 tff(greater_type, type, (
% 0.20/0.40 greater: ( $i * $i ) > $o)).
% 0.20/0.40 tff(geq_type, type, (
% 0.20/0.40 geq: ( $i * $i ) > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[Vd432: $i, Vd433: $i, Vd434: $i] : refl((vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(281, 0), 0)'')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,(
% 0.20/0.40 ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))) | (vmul(vd518, vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))) = vplus(vmul(vd518, vd520), vmul(vd518, tptp_fun_Vd196_1(vd519, vd520))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (vmul(vd518, vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))) = vplus(vmul(vd518, vd520), vmul(vd518, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (^[Vd193: $i, Vd194: $i] : refl((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (^[Vd193: $i, Vd194: $i] : rewrite((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[13, 11])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[Vd193: $i, Vd194: $i] : trans(monotonicity(rewrite((greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))) <=> (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))), rewrite((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196))) <=> ![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(18,axiom,(![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 11), 1)'')).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.41 tff(20,plain,(
% 0.20/0.41 ![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))) | (~(greater(vd519, vd520) | ![Vd196: $i] : (~(vd519 = vplus(vd520, Vd196)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~((~((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))) | (~(greater(vd519, vd520) | ![Vd196: $i] : (~(vd519 = vplus(vd520, Vd196))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (((~((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))) | (~(greater(vd519, vd520) | ![Vd196: $i] : (~(vd519 = vplus(vd520, Vd196)))))) | ((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (^[Vd244: $i, Vd245: $i] : refl((geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (^[Vd244: $i, Vd245: $i] : rewrite((geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> (greater(Vd245, Vd244) | (Vd245 = Vd244))) <=> ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.41 tff(32,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)'')).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.41 tff(35,plain,(
% 0.20/0.41 ![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,assumption,(~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))), introduced(assumption)).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (((~geq(vd519, vd520)) | (~greater(vd517, vd518))) | geq(vd519, vd520)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (geq(vd519, vd520)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~(geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))) | (~geq(vd519, vd520)) | ((vd519 = vd520) | greater(vd519, vd520))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~(geq(vd519, vd520) <=> ((vd519 = vd520) | greater(vd519, vd520)))) | ((vd519 = vd520) | greater(vd519, vd520))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((vd519 = vd520) | greater(vd519, vd520)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 38])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (((~geq(vd519, vd520)) | (~greater(vd517, vd518))) | greater(vd517, vd518)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (greater(vd517, vd518)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,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)'')).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.41 tff(57,plain,(
% 0.20/0.41 ![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : ((~(greater(Vd504, Vd505) & greater(Vd501, Vd502))) | greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![Vd501: $i, Vd502: $i, Vd504: $i, Vd505: $i] : (greater(vmul(Vd501, Vd504), vmul(Vd502, Vd505)) | (~greater(Vd504, Vd505)) | (~greater(Vd501, Vd502)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) <=> (~greater(vmul(vd517, vd519), vmul(vd518, vd520)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(61,axiom,(~greater(vmul(vd517, vd519), vmul(vd518, vd520))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(scope(318)), 525, 0)'')).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (~greater(vmul(vd517, vd519), vmul(vd518, vd520))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~![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)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![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))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~greater(vd519, vd520)) | (~greater(vd517, vd518))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (~greater(vd519, vd520)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 46])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~((vd519 = vd520) | greater(vd519, vd520))) | (vd519 = vd520) | greater(vd519, vd520)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~((vd519 = vd520) | greater(vd519, vd520))) | (vd519 = vd520)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (vd519 = vd520),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 44])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (vd520 = vd519),
% 0.20/0.41 inference(symmetry,[status(thm)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (vmul(vd517, vd520) = vmul(vd517, vd519)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (greater(vmul(vd517, vd520), vmul(vd518, vd520)) <=> greater(vmul(vd517, vd519), vmul(vd518, vd520))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (greater(vmul(vd517, vd519), vmul(vd518, vd520)) <=> greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.20/0.41 inference(symmetry,[status(thm)],[73])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) <=> (~greater(vmul(vd517, vd520), vmul(vd518, vd520)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (~greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 75])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.42 tff(82,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)'')).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.42 tff(85,plain,(
% 0.20/0.42 ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd517, vd518)) | greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (greater(vmul(vd517, vd520), vmul(vd518, vd520))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 46, 86])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 76])).
% 0.20/0.42 tff(92,plain,((~geq(vd519, vd520)) | (~greater(vd517, vd518))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((geq(vd519, vd520) & greater(vd517, vd518)) <=> (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) <=> (~((~greater(vd519, vd520)) | (~geq(vd517, vd518))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[95, 94])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[96, 93])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))) <=> ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,axiom,((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''dis(antec(scope(318)))'')).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 98])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 98])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[103, 98])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 98])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 ((greater(vd519, vd520) & geq(vd517, vd518)) | (geq(vd519, vd520) & greater(vd517, vd518))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 98])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 ((~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))) | (~((~geq(vd519, vd520)) | (~greater(vd517, vd518))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (~((~greater(vd519, vd520)) | (~geq(vd517, vd518)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[108, 92])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (((~greater(vd519, vd520)) | (~geq(vd517, vd518))) | greater(vd519, vd520)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (greater(vd519, vd520)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))) | (~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~((~greater(vd519, vd520)) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))))) | (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (vd519 = vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 26])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (vplus(vd520, tptp_fun_Vd196_1(vd519, vd520)) = vd519),
% 0.20/0.42 inference(symmetry,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[116, 36])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (((~greater(vd519, vd520)) | (~geq(vd517, vd518))) | geq(vd517, vd518)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (geq(vd517, vd518)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[118, 109])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 ((~(geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))) | (~geq(vd517, vd518)) | ((vd517 = vd518) | greater(vd517, vd518))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 ((~(geq(vd517, vd518) <=> ((vd517 = vd518) | greater(vd517, vd518)))) | ((vd517 = vd518) | greater(vd517, vd518))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 ((vd517 = vd518) | greater(vd517, vd518)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[121, 117])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (~greater(vd517, vd518)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[66, 111])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((~((vd517 = vd518) | greater(vd517, vd518))) | (vd517 = vd518) | greater(vd517, vd518)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~((vd517 = vd518) | greater(vd517, vd518))) | (vd517 = vd518)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (vd517 = vd518),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (vd518 = vd517),
% 0.20/0.42 inference(symmetry,[status(thm)],[126])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (vmul(vd518, vplus(vd520, tptp_fun_Vd196_1(vd519, vd520))) = vmul(vd517, vd519)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[127, 115])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (vmul(vd517, vd519) = vmul(vd518, vplus(vd520, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[128])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (vmul(vd517, vd519) = vplus(vmul(vd518, vd520), vmul(vd518, tptp_fun_Vd196_1(vd519, vd520)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[129, 9])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) | (vmul(vd517, vd519) = vplus(vmul(vd518, vd520), tptp_fun_Vd196_1(vmul(vd517, vd519), vmul(vd518, vd520)))))) | (~(greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (~((~((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) | (vmul(vd517, vd519) = vplus(vmul(vd518, vd520), tptp_fun_Vd196_1(vmul(vd517, vd519), vmul(vd518, vd520)))))) | (~(greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 22])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~((~greater(vmul(vd517, vd519), vmul(vd518, vd520))) | (vmul(vd517, vd519) = vplus(vmul(vd518, vd520), tptp_fun_Vd196_1(vmul(vd517, vd519), vmul(vd518, vd520)))))) | (~(greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))))) | (greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~(greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196))))) | greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 ((~(greater(vmul(vd517, vd519), vmul(vd518, vd520)) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196))))) | ![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 62])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[136, 134])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 ((~![Vd196: $i] : (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), Vd196)))) | (~(vmul(vd517, vd519) = vplus(vmul(vd518, vd520), vmul(vd518, tptp_fun_Vd196_1(vd519, vd520)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[138, 137, 130])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------