%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM845+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:22:12 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM845+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:03:31 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(vplus_type, type, (
% 0.18/0.37 vplus: ( $i * $i ) > $i)).
% 0.18/0.37 tff(vsucc_type, type, (
% 0.18/0.37 vsucc: $i > $i)).
% 0.18/0.37 tff(tptp_fun_Vd416_0_type, type, (
% 0.18/0.37 tptp_fun_Vd416_0: $i)).
% 0.18/0.37 tff(vmul_type, type, (
% 0.18/0.37 vmul: ( $i * $i ) > $i)).
% 0.18/0.37 tff(vd411_type, type, (
% 0.18/0.37 vd411: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[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)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (^[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)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.37 tff(6,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 0)'')).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,(
% 0.18/0.37 ![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))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[8])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ((~![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)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 ((~![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)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 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/sandbox/benchmark/theBenchmark.p',''qu(ind(267), imp(267))'')).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (~![Vd416: $i] : ((~(vmul(vsucc(vd411), Vd416) = vplus(vmul(vd411, Vd416), Vd416))) | (vmul(vsucc(vd411), vsucc(Vd416)) = vplus(vmul(vd411, vsucc(Vd416)), vsucc(Vd416))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.18/0.37 tff(18,plain,(
% 0.18/0.37 ~((~(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))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[17])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0)),
% 0.18/0.37 inference(or_elim,[status(thm)],[18])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (((~![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))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 ((~![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))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 ((~![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)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[22, 19, 10])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.38 tff(29,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 1)'')).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.38 tff(32,plain,(
% 0.18/0.38 ![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))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[31])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![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))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (((~![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))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 ((~![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))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ((~![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)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0))) = vplus(vplus(vmul(vd411, Vd416!0), vd411), vsucc(Vd416!0))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[36, 19, 33])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (^[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))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (^[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))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.38 tff(43,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 2)'')).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.18/0.38 tff(46,plain,(
% 0.18/0.38 ![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)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[45])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~![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)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 ((~![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)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 ((~![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))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0))) = vplus(vmul(vd411, Vd416!0), vplus(vd411, vsucc(Vd416!0)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[50, 19, 47])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (^[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))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (![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)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.39 tff(57,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 3)'')).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.18/0.39 tff(60,plain,(
% 0.18/0.39 ![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)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[59])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (((~![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 ((~![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)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((~![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0)) = vplus(vmul(vd411, Vd416!0), vsucc(vplus(vd411, Vd416!0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[64, 19, 61])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.39 tff(71,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 4)'')).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.18/0.39 tff(74,plain,(
% 0.18/0.39 ![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))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[73])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (((~![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))))) | ((~(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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 ((~![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))))) | ((~(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))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 ((~![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))))) | (~(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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411))) = vplus(vmul(vd411, Vd416!0), vplus(vsucc(vd411), Vd416!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[78, 19, 75])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.40 tff(85,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 5)'')).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.40 tff(88,plain,(
% 0.18/0.40 ![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)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[87])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (((~![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)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 ((~![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)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411)) = vplus(vmul(vd411, Vd416!0), vplus(Vd416!0, vsucc(vd411)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[92, 19, 89])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)) = vplus(vplus(vmul(vd411, Vd416!0), Vd416!0), vsucc(vd411))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.18/0.40 tff(100,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/sandbox/benchmark/theBenchmark.p',''ass(cond(conseq(263), 1), 7)'')).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.18/0.40 tff(103,plain,(
% 0.18/0.40 ![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[102])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (((~![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 ((~![Vd413: $i] : ((~(vmul(vsucc(vd411), Vd413) = vplus(vmul(vd411, Vd413), Vd413))) | (vmul(vsucc(vd411), vsucc(Vd413)) = vplus(vmul(vsucc(vd411), Vd413), vsucc(vd411))))) | (~(vmul(vsucc(vd411), Vd416!0) = vplus(vmul(vd411, Vd416!0), Vd416!0))) | (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vsucc(vd411), Vd416!0), vsucc(vd411))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[107, 19, 104])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0))),
% 0.18/0.40 inference(transitivity,[status(thm)],[108, 94, 93, 79, 65, 51, 37, 23])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (~(vmul(vsucc(vd411), vsucc(Vd416!0)) = vplus(vmul(vd411, vsucc(Vd416!0)), vsucc(Vd416!0)))),
% 0.18/0.40 inference(or_elim,[status(thm)],[18])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------