TSTP Solution File: NUM842+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM842+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 13:12:12 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM842+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.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 14:45:08 EDT 2022
% 0.12/0.33 % 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(vplus_type, type, (
% 0.19/0.40 vplus: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_Vd196_1_type, type, (
% 0.19/0.40 tptp_fun_Vd196_1: ( $i * $i ) > $i)).
% 0.19/0.40 tff(vd356_type, type, (
% 0.19/0.40 vd356: $i)).
% 0.19/0.40 tff(vd355_type, type, (
% 0.19/0.40 vd355: $i)).
% 0.19/0.40 tff(vd354_type, type, (
% 0.19/0.40 vd354: $i)).
% 0.19/0.40 tff(vd353_type, type, (
% 0.19/0.40 vd353: $i)).
% 0.19/0.40 tff(greater_type, type, (
% 0.19/0.40 greater: ( $i * $i ) > $o)).
% 0.19/0.40 tff(geq_type, type, (
% 0.19/0.40 geq: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[Vd46: $i, Vd47: $i, Vd48: $i] : refl((vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,axiom,(![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(33, 0), 0)'')).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.40 tff(6,plain,(
% 0.19/0.40 ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[5])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vd355, vd356)) = vplus(vd354, vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vd355, vd356)) = vplus(vd354, vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (vplus(vd354, vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vd355, vd356))),
% 0.19/0.40 inference(symmetry,[status(thm)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[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))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (^[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)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(19,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)'')).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~![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)))))))) | (~((~((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))) | (~(greater(vd355, vd356) | ![Vd196: $i] : (~(vd355 = vplus(vd356, Vd196)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (~((~((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))) | (~(greater(vd355, vd356) | ![Vd196: $i] : (~(vd355 = vplus(vd356, Vd196))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (((~((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))) | (~(greater(vd355, vd356) | ![Vd196: $i] : (~(vd355 = vplus(vd356, Vd196)))))) | ((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,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(29,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)],[28])).
% 0.19/0.41 tff(30,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(31,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(32,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)],[31])).
% 0.19/0.41 tff(33,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)'')).
% 0.19/0.41 tff(34,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)],[33, 32])).
% 0.19/0.41 tff(35,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)],[34, 30])).
% 0.19/0.41 tff(36,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)],[35])).
% 0.19/0.41 tff(37,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)],[36, 29])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd355, vd356) <=> ((vd355 = vd356) | greater(vd355, vd356)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (geq(vd355, vd356) <=> ((vd355 = vd356) | greater(vd355, vd356))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,assumption,(~((~geq(vd355, vd356)) | (~greater(vd353, vd354)))), introduced(assumption)).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~geq(vd355, vd356)) | (~greater(vd353, vd354))) | geq(vd355, vd356)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (geq(vd355, vd356)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~(geq(vd355, vd356) <=> ((vd355 = vd356) | greater(vd355, vd356)))) | (~geq(vd355, vd356)) | ((vd355 = vd356) | greater(vd355, vd356))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~(geq(vd355, vd356) <=> ((vd355 = vd356) | greater(vd355, vd356)))) | ((vd355 = vd356) | greater(vd355, vd356))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ((vd355 = vd356) | greater(vd355, vd356)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 39])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (((~geq(vd355, vd356)) | (~greater(vd353, vd354))) | greater(vd353, vd354)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (greater(vd353, vd354)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 40])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (^[Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : refl((greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))) <=> (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))) <=> ![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : trans(monotonicity(trans(monotonicity(rewrite((greater(Vd340, Vd341) & greater(Vd337, Vd338)) <=> (~((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))))), ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) <=> (~(~((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))))))), rewrite((~(~((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))))) <=> ((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))), ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) <=> ((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))))), (((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> (((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))))), rewrite((((~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))), (((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> ![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> ![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : rewrite(((greater(Vd340, Vd341) & greater(Vd337, Vd338)) => greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((greater(Vd340, Vd341) & greater(Vd337, Vd338)) => greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341))) <=> ![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,axiom,(![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((greater(Vd340, Vd341) & greater(Vd337, Vd338)) => greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(209, 0), 0)'')).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.41 tff(58,plain,(
% 0.19/0.41 ![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : ((~(greater(Vd340, Vd341) & greater(Vd337, Vd338))) | greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~greater(vplus(vd353, vd355), vplus(vd354, vd356))) <=> (~greater(vplus(vd353, vd355), vplus(vd354, vd356)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,axiom,(~greater(vplus(vd353, vd355), vplus(vd354, vd356))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(218), 361, 0)'')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (~greater(vplus(vd353, vd355), vplus(vd354, vd356))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (((~![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))) | (greater(vplus(vd353, vd355), vplus(vd354, vd356)) | (~greater(vd355, vd356)) | (~greater(vd353, vd354)))) <=> ((~![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))) | greater(vplus(vd353, vd355), vplus(vd354, vd356)) | (~greater(vd355, vd356)) | (~greater(vd353, vd354)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))) | (greater(vplus(vd353, vd355), vplus(vd354, vd356)) | (~greater(vd355, vd356)) | (~greater(vd353, vd354)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 ((~![Vd337: $i, Vd338: $i, Vd340: $i, Vd341: $i] : (greater(vplus(Vd337, Vd340), vplus(Vd338, Vd341)) | (~greater(Vd340, Vd341)) | (~greater(Vd337, Vd338)))) | greater(vplus(vd353, vd355), vplus(vd354, vd356)) | (~greater(vd355, vd356)) | (~greater(vd353, vd354))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~greater(vd355, vd356)) | (~greater(vd353, vd354))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 63, 60])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (~greater(vd355, vd356)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[67, 47])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~((vd355 = vd356) | greater(vd355, vd356))) | (vd355 = vd356) | greater(vd355, vd356)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 ((~((vd355 = vd356) | greater(vd355, vd356))) | (vd355 = vd356)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (vd355 = vd356),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 45])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (vd356 = vd355),
% 0.19/0.41 inference(symmetry,[status(thm)],[71])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (vplus(vd353, vd356) = vplus(vd353, vd355)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (greater(vplus(vd353, vd356), vplus(vd354, vd356)) <=> greater(vplus(vd353, vd355), vplus(vd354, vd356))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (greater(vplus(vd353, vd355), vplus(vd354, vd356)) <=> greater(vplus(vd353, vd356), vplus(vd354, vd356))),
% 0.19/0.41 inference(symmetry,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~greater(vplus(vd353, vd355), vplus(vd354, vd356))) <=> (~greater(vplus(vd353, vd356), vplus(vd354, vd356)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (~greater(vplus(vd353, vd356), vplus(vd354, vd356))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite((greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.41 tff(83,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 2)'')).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.41 tff(86,plain,(
% 0.19/0.41 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[85])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd353, vd354)) | greater(vplus(vd353, vd356), vplus(vd354, vd356)))) <=> ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd353, vd354)) | greater(vplus(vd353, vd356), vplus(vd354, vd356)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd353, vd354)) | greater(vplus(vd353, vd356), vplus(vd354, vd356)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd353, vd354)) | greater(vplus(vd353, vd356), vplus(vd354, vd356))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (greater(vplus(vd353, vd356), vplus(vd354, vd356))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 47, 87])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 77])).
% 0.19/0.41 tff(93,plain,((~geq(vd355, vd356)) | (~greater(vd353, vd354))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (((~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))) | (~((~geq(vd355, vd356)) | (~greater(vd353, vd354))))) <=> ((~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))) | (~((~geq(vd355, vd356)) | (~greater(vd353, vd354)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((geq(vd355, vd356) & greater(vd353, vd354)) <=> (~((~geq(vd355, vd356)) | (~greater(vd353, vd354))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) <=> (~((~greater(vd355, vd356)) | (~geq(vd353, vd354))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))) <=> ((~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))) | (~((~geq(vd355, vd356)) | (~greater(vd353, vd354)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[96, 95])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))) <=> ((~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))) | (~((~geq(vd355, vd356)) | (~greater(vd353, vd354)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[97, 94])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))) <=> ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(100,axiom,((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''dis(antec(218))'')).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[102, 99])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 99])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[105, 99])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ((greater(vd355, vd356) & geq(vd353, vd354)) | (geq(vd355, vd356) & greater(vd353, vd354))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 99])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))) | (~((~geq(vd355, vd356)) | (~greater(vd353, vd354))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (~((~greater(vd355, vd356)) | (~geq(vd353, vd354)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[109, 93])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (((~greater(vd355, vd356)) | (~geq(vd353, vd354))) | greater(vd355, vd356)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (greater(vd355, vd356)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 ((~((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))) | (~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ((~((~greater(vd355, vd356)) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))))) | (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (vd355 = vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[114, 27])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)) = vd355),
% 0.19/0.42 inference(symmetry,[status(thm)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 ((~![Vd244: $i, Vd245: $i] : (geq(Vd245, Vd244) <=> ((Vd245 = Vd244) | greater(Vd245, Vd244)))) | (geq(vd353, vd354) <=> ((vd353 = vd354) | greater(vd353, vd354)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (geq(vd353, vd354) <=> ((vd353 = vd354) | greater(vd353, vd354))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[117, 37])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (((~greater(vd355, vd356)) | (~geq(vd353, vd354))) | geq(vd353, vd354)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (geq(vd353, vd354)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 110])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((~(geq(vd353, vd354) <=> ((vd353 = vd354) | greater(vd353, vd354)))) | (~geq(vd353, vd354)) | ((vd353 = vd354) | greater(vd353, vd354))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ((~(geq(vd353, vd354) <=> ((vd353 = vd354) | greater(vd353, vd354)))) | ((vd353 = vd354) | greater(vd353, vd354))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 ((vd353 = vd354) | greater(vd353, vd354)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (~greater(vd353, vd354)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[67, 112])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((~((vd353 = vd354) | greater(vd353, vd354))) | (vd353 = vd354) | greater(vd353, vd354)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((~((vd353 = vd354) | greater(vd353, vd354))) | (vd353 = vd354)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (vd353 = vd354),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (vd354 = vd353),
% 0.19/0.42 inference(symmetry,[status(thm)],[127])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (vplus(vd354, vplus(vd356, tptp_fun_Vd196_1(vd355, vd356))) = vplus(vd353, vd355)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[128, 116])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (vplus(vd353, vd355) = vplus(vd354, vplus(vd356, tptp_fun_Vd196_1(vd355, vd356)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[129])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (vplus(vd353, vd355) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vd355, vd356))),
% 0.19/0.42 inference(transitivity,[status(thm)],[130, 10])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 ((~![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(vplus(vd353, vd355), vplus(vd354, vd356))) | (vplus(vd353, vd355) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vplus(vd353, vd355), vplus(vd354, vd356)))))) | (~(greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (~((~((~greater(vplus(vd353, vd355), vplus(vd354, vd356))) | (vplus(vd353, vd355) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vplus(vd353, vd355), vplus(vd354, vd356)))))) | (~(greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 23])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (((~((~greater(vplus(vd353, vd355), vplus(vd354, vd356))) | (vplus(vd353, vd355) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vplus(vd353, vd355), vplus(vd354, vd356)))))) | (~(greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))))) | (greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196))))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((~(greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196))))) | greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~(greater(vplus(vd353, vd355), vplus(vd354, vd356)) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196))))) | ![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 63])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 ((~![Vd196: $i] : (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), Vd196)))) | (~(vplus(vd353, vd355) = vplus(vplus(vd354, vd356), tptp_fun_Vd196_1(vd355, vd356))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 138, 131])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------