%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM849+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 05:22:13 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM849+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:03:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(vmul_type, type, (
% 0.20/0.37 vmul: ( $i * $i ) > $i)).
% 0.20/0.37 tff(vsucc_type, type, (
% 0.20/0.37 vsucc: $i > $i)).
% 0.20/0.37 tff(tptp_fun_Vd454_0_type, type, (
% 0.20/0.37 tptp_fun_Vd454_0: $i)).
% 0.20/0.37 tff(vd449_type, type, (
% 0.20/0.37 vd449: $i)).
% 0.20/0.37 tff(vd448_type, type, (
% 0.20/0.37 vd448: $i)).
% 0.20/0.37 tff(vplus_type, type, (
% 0.20/0.37 vplus: ( $i * $i ) > $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[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))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (^[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))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.37 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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 0)'')).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,(
% 0.20/0.37 ![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)))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 ((~![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))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((~![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))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 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/sandbox/benchmark/theBenchmark.p',''qu(ind(296), imp(296))'')).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (~![Vd454: $i] : ((~(vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ~((~(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)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0))),
% 0.20/0.38 inference(or_elim,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![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)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![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)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[22, 19, 10])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.38 tff(29,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 1)'')).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.38 tff(32,plain,(
% 0.20/0.38 ![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))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (((~![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![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))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd454!0), vd449))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 19, 33])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd454!0)), vmul(vd448, vd449))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.39 tff(44,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(292), 1), 3)'')).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.39 tff(47,plain,(
% 0.20/0.39 ![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))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[46])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (((~![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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~![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))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~![Vd451: $i] : ((~(vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)))) | (vmul(vmul(vd448, vd449), vsucc(Vd451)) = vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449))))) | (~(vmul(vmul(vd448, vd449), Vd454!0) = vmul(vd448, vmul(vd449, Vd454!0)))) | (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vplus(vmul(vmul(vd448, vd449), Vd454!0), vmul(vd448, vd449))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[51, 19, 48])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[52, 38, 37, 23])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (~(vmul(vmul(vd448, vd449), vsucc(Vd454!0)) = vmul(vd448, vmul(vd449, vsucc(Vd454!0))))),
% 0.20/0.39 inference(or_elim,[status(thm)],[18])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------