TSTP Solution File: NUM849+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM849+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 13:12:16 EDT 2022
% Result : Theorem 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 15:20:14 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.41 % SZS status Theorem
% 0.22/0.41 % SZS output start Proof
% 0.22/0.41 tff(vmul_type, type, (
% 0.22/0.41 vmul: ( $i * $i ) > $i)).
% 0.22/0.41 tff(vsucc_type, type, (
% 0.22/0.41 vsucc: $i > $i)).
% 0.22/0.41 tff(tptp_fun_Vd454_0_type, type, (
% 0.22/0.41 tptp_fun_Vd454_0: $i)).
% 0.22/0.41 tff(vd449_type, type, (
% 0.22/0.41 vd449: $i)).
% 0.22/0.41 tff(vd448_type, type, (
% 0.22/0.41 vd448: $i)).
% 0.22/0.41 tff(vplus_type, type, (
% 0.22/0.41 vplus: ( $i * $i ) > $i)).
% 0.22/0.41 tff(1,plain,
% 0.22/0.41 (^[Vd451: $i] : refl(((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(2,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.41 tff(3,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(4,plain,
% 0.22/0.41 (^[Vd451: $i] : rewrite(((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(5,plain,
% 0.22/0.41 (![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.41 tff(6,axiom,(![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 0)'')).
% 0.22/0.41 tff(7,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.22/0.41 tff(8,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.41 tff(9,plain,(
% 0.22/0.41 ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[8])).
% 0.22/0.41 tff(10,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.41 tff(11,plain,
% 0.22/0.41 ((~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))) <=> (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(12,plain,
% 0.22/0.41 ((~![Vd454: $i] : ((vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454))) => (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))) <=> (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(13,axiom,(~![Vd454: $i] : ((vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454))) => (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''qu(ind(296), imp(296))'')).
% 0.22/0.41 tff(14,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.41 tff(15,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.22/0.41 tff(16,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.22/0.41 tff(17,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.22/0.41 tff(18,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.22/0.41 tff(19,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.22/0.41 tff(20,plain,
% 0.22/0.41 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.22/0.41 tff(21,plain,(
% 0.22/0.41 ~((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[20])).
% 0.22/0.41 tff(22,plain,
% 0.22/0.41 (vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0))),
% 0.22/0.41 inference(or_elim,[status(thm)],[21])).
% 0.22/0.41 tff(23,plain,
% 0.22/0.41 (((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))))) <=> ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(24,plain,
% 0.22/0.41 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(25,plain,
% 0.22/0.41 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451)))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.22/0.41 tff(26,plain,
% 0.22/0.41 (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[25, 22, 10])).
% 0.22/0.41 tff(27,plain,
% 0.22/0.41 (^[Vd451: $i] : refl(((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(28,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.22/0.41 tff(29,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(30,plain,
% 0.22/0.41 (^[Vd451: $i] : rewrite(((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(31,plain,
% 0.22/0.41 (![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.22/0.41 tff(32,axiom,(![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 1)'')).
% 0.22/0.41 tff(33,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.41 tff(34,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.41 tff(35,plain,(
% 0.22/0.41 ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[34])).
% 0.22/0.41 tff(36,plain,
% 0.22/0.41 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449))))) <=> ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[39, 22, 36])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.42 (^[Vd451: $i] : refl(((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(42,plain,
% 0.22/0.42 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.42 tff(43,plain,
% 0.22/0.42 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(44,plain,
% 0.22/0.42 (^[Vd451: $i] : rewrite(((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(45,plain,
% 0.22/0.42 (![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.42 tff(46,axiom,(![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 2)'')).
% 0.22/0.42 tff(47,plain,
% 0.22/0.42 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.42 tff(48,plain,
% 0.22/0.42 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.22/0.42 tff(49,plain,(
% 0.22/0.42 ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[48])).
% 0.22/0.42 tff(50,plain,
% 0.22/0.42 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.22/0.42 tff(51,plain,
% 0.22/0.42 (((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449))))) <=> ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(52,plain,
% 0.22/0.42 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(53,plain,
% 0.22/0.42 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.42 tff(54,plain,
% 0.22/0.42 (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[53, 22, 50])).
% 0.22/0.42 tff(55,plain,
% 0.22/0.42 (^[Vd451: $i] : refl(((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.22/0.43 tff(57,plain,
% 0.22/0.43 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(58,plain,
% 0.22/0.43 (^[Vd451: $i] : rewrite(((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))) <=> ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(59,plain,
% 0.22/0.43 (![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)))) <=> ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.43 tff(60,axiom,(![Vd451: $i] : ((vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451))) => (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 3)'')).
% 0.22/0.43 tff(61,plain,
% 0.22/0.43 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.43 tff(62,plain,
% 0.22/0.43 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.22/0.43 tff(63,plain,(
% 0.22/0.43 ![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[62])).
% 0.22/0.43 tff(64,plain,
% 0.22/0.43 (![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.22/0.43 tff(65,plain,
% 0.22/0.43 (((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449))))) <=> ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(66,plain,
% 0.22/0.43 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))) | ((~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(67,plain,
% 0.22/0.43 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.22/0.43 tff(68,plain,
% 0.22/0.43 (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[67, 22, 64])).
% 0.22/0.43 tff(69,plain,
% 0.22/0.43 (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))),
% 0.22/0.43 inference(transitivity,[status(thm)],[68, 54, 40, 26])).
% 0.22/0.43 tff(70,plain,
% 0.22/0.43 (~(vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0))))),
% 0.22/0.43 inference(or_elim,[status(thm)],[21])).
% 0.22/0.43 tff(71,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.22/0.43 % SZS output end Proof
%------------------------------------------------------------------------------