TSTP Solution File: NUM852+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 13:12:17 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM852+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 : n026.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 15:38:23 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(vplus_type, type, (
% 0.19/0.39 vplus: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vmul_type, type, (
% 0.19/0.39 vmul: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vd469_type, type, (
% 0.19/0.39 vd469: $i)).
% 0.19/0.39 tff(vskolem9_type, type, (
% 0.19/0.39 vskolem9: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vd480_type, type, (
% 0.19/0.39 vd480: $i)).
% 0.19/0.39 tff(vd481_type, type, (
% 0.19/0.39 vd481: $i)).
% 0.19/0.39 tff(greater_type, type, (
% 0.19/0.39 greater: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Vd196_1_type, type, (
% 0.19/0.39 tptp_fun_Vd196_1: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[Vd470: $i, Vd471: $i] : refl(((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))) <=> ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (^[Vd470: $i, Vd471: $i] : rewrite((greater(Vd470, Vd471) => (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))) <=> ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : (greater(Vd470, Vd471) => (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.39 tff(6,axiom,(![Vd470: $i, Vd471: $i] : (greater(Vd470, Vd471) => (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(302, 0), 1)'')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,(
% 0.19/0.39 ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[8])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (greater(vd481, vd480) <=> greater(vd481, vd480)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,axiom,(greater(vd481, vd480)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq_conjunct1(conseq(304)), 483, 0)'')).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (greater(vd481, vd480)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))) | ((~greater(vd481, vd480)) | (vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))))) <=> ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))) | (~greater(vd481, vd480)) | (vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))) | ((~greater(vd481, vd480)) | (vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469))))) | (~greater(vd481, vd480)) | (vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (^[Vd470: $i, Vd471: $i] : refl(((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))) <=> ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (^[Vd470: $i, Vd471: $i] : rewrite((greater(Vd470, Vd471) => (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))) <=> ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : (greater(Vd470, Vd471) => (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469))) <=> ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.40 tff(23,axiom,(![Vd470: $i, Vd471: $i] : (greater(Vd470, Vd471) => (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(302, 0), 2)'')).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.40 tff(26,plain,(
% 0.19/0.40 ![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))) | ((~greater(vd481, vd480)) | (vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469)))) <=> ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))) | (~greater(vd481, vd480)) | (vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))) | ((~greater(vd481, vd480)) | (vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~![Vd470: $i, Vd471: $i] : ((~greater(Vd470, Vd471)) | (vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469)))) | (~greater(vd481, vd480)) | (vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 13, 27])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (vmul(vd481, vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))),
% 0.19/0.40 inference(transitivity,[status(thm)],[31, 17])).
% 0.19/0.40 tff(33,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(34,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)],[33])).
% 0.19/0.40 tff(35,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(36,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)],[35])).
% 0.19/0.40 tff(37,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)],[36, 34])).
% 0.19/0.40 tff(38,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(39,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)],[38])).
% 0.19/0.40 tff(40,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(41,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(42,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)],[41, 40])).
% 0.19/0.40 tff(43,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)],[42])).
% 0.19/0.40 tff(44,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)],[43, 39])).
% 0.19/0.40 tff(45,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)],[44, 37])).
% 0.19/0.40 tff(46,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(vmul(vd481, vd469), vmul(vd480, vd469))) | (vmul(vd481, vd469) = vplus(vmul(vd480, vd469), tptp_fun_Vd196_1(vmul(vd481, vd469), vmul(vd480, vd469)))))) | (~(greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (~((~((~greater(vmul(vd481, vd469), vmul(vd480, vd469))) | (vmul(vd481, vd469) = vplus(vmul(vd480, vd469), tptp_fun_Vd196_1(vmul(vd481, vd469), vmul(vd480, vd469)))))) | (~(greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (((~((~greater(vmul(vd481, vd469), vmul(vd480, vd469))) | (vmul(vd481, vd469) = vplus(vmul(vd480, vd469), tptp_fun_Vd196_1(vmul(vd481, vd469), vmul(vd480, vd469)))))) | (~(greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))))) | (greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((~greater(vmul(vd481, vd469), vmul(vd480, vd469))) <=> (~greater(vmul(vd481, vd469), vmul(vd480, vd469)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,axiom,(~greater(vmul(vd481, vd469), vmul(vd480, vd469))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)'')).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (~greater(vmul(vd481, vd469), vmul(vd480, vd469))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~(greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196))))) | greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~(greater(vmul(vd481, vd469), vmul(vd480, vd469)) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196))))) | ![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 49])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~![Vd196: $i] : (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), Vd196)))) | (~(vmul(vd481, vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 55, 32])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------