TSTP Solution File: NUM845+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 13:12:14 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM845+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n021.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Sep 2 15:18:29 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(vplus_type, type, (
% 0.12/0.39 vplus: ( $i * $i ) > $i)).
% 0.12/0.39 tff(vsucc_type, type, (
% 0.12/0.39 vsucc: $i > $i)).
% 0.12/0.39 tff(tptp_fun_Vd416_0_type, type, (
% 0.12/0.39 tptp_fun_Vd416_0: $i)).
% 0.12/0.39 tff(vmul_type, type, (
% 0.12/0.39 vmul: ( $i * $i ) > $i)).
% 0.12/0.39 tff(vd411_type, type, (
% 0.12/0.39 vd411: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 6)'')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))) <=> (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((~![Vd416: $i] : ((vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416)) => (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))) <=> (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,axiom,(~![Vd416: $i] : ((vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416)) => (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''qu(ind(267), imp(267))'')).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.12/0.39 tff(21,plain,(
% 0.12/0.39 ~((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[25, 22, 10])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))),
% 0.12/0.39 inference(symmetry,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.39 tff(33,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 5)'')).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.12/0.39 tff(36,plain,(
% 0.12/0.39 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[35])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), Vd413), vsucc(vd411)) = vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[40, 22, 37])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))),
% 0.12/0.39 inference(symmetry,[status(thm)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.40 tff(48,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 4)'')).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.40 tff(51,plain,(
% 0.12/0.40 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[50])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(Vd413, vsucc(vd411))) = vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[55, 22, 52])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.40 tff(63,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 3)'')).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.40 tff(66,plain,(
% 0.20/0.40 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[65])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vsucc(vd411), Vd413)) = vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 22, 67])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))),
% 0.20/0.40 inference(symmetry,[status(thm)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.40 tff(78,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 2)'')).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.40 tff(81,plain,(
% 0.20/0.40 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[80])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vsucc(vplus(vd411, Vd413))) = vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413)))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[85, 22, 82])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[86])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.40 tff(93,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 1)'')).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.40 tff(96,plain,(
% 0.20/0.40 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[95])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vmul(vd411, Vd413), vplus(vd411, vsucc(Vd413))) = vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 22, 97])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.41 tff(108,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 0)'')).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.41 tff(111,plain,(
% 0.20/0.41 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vplus(vplus(vmul(vd411, Vd413), vd411), vsucc(Vd413)) = vplus(vmul(vd411, vsucc(Vd413)), vsucc(Vd413))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[115, 22, 112])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))),
% 0.20/0.41 inference(symmetry,[status(thm)],[116])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))),
% 0.20/0.41 inference(transitivity,[status(thm)],[117, 102, 87, 72, 57, 42, 27])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))) <=> (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))) <=> (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[119])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (^[Vd413: $i] : refl(((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (^[Vd413: $i] : rewrite(((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))) <=> ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411)))) <=> ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.41 tff(126,axiom,(![Vd413: $i] : ((vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413)) => (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 7)'')).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.20/0.41 tff(129,plain,(
% 0.20/0.41 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[128])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))))) <=> ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))) | ((~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[133, 22, 130])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[134, 120])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 (~(vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[21])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------