%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM224_1 : TPTP v9.3.0. Released v9.3.0.
% 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 : Tue May 5 06:23:01 PM UTC 2026
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM224_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 19:06:40 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(vptchecksimple_type, type, (
% 0.20/0.41 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.20/0.41 tff(vNat_type, type, (
% 0.20/0.41 vNat: vTy)).
% 0.20/0.41 tff(tptp_fun_Vnv_64_type, type, (
% 0.20/0.41 tptp_fun_Vnv_64: vTerm)).
% 0.20/0.41 tff(tptp_fun_VT_63_type, type, (
% 0.20/0.41 tptp_fun_VT_63: vTy)).
% 0.20/0.41 tff(tptp_fun_Vtres_62_type, type, (
% 0.20/0.41 tptp_fun_Vtres_62: vTerm)).
% 0.20/0.41 tff(vPred_type, type, (
% 0.20/0.41 vPred: vTerm > vTerm)).
% 0.20/0.41 tff(vSucc_type, type, (
% 0.20/0.41 vSucc: vTerm > vTerm)).
% 0.20/0.41 tff(vt1_type, type, (
% 0.20/0.41 vt1: vTerm)).
% 0.20/0.41 tff(vsomeTerm_type, type, (
% 0.20/0.41 vsomeTerm: vTerm > vOptTerm)).
% 0.20/0.41 tff(vreduce_type, type, (
% 0.20/0.41 vreduce: vTerm > vOptTerm)).
% 0.20/0.41 tff(vZero_type, type, (
% 0.20/0.41 vZero: vTerm)).
% 0.20/0.41 tff(visNV_type, type, (
% 0.20/0.41 visNV: vTerm > $o)).
% 0.20/0.41 tff(vgetTerm_type, type, (
% 0.20/0.41 vgetTerm: vOptTerm > vTerm)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))) <=> (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : (((((visNV(Vnv) & (~(vt1 = vZero))) & (vt1 = vSucc(Vnv))) & vptchecksimple(vPred(vt1), VT)) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))) <=> (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,axiom,(~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : (((((visNV(Vnv) & (~(vt1 = vZero))) & (vt1 = vSucc(Vnv))) & vptchecksimple(vPred(vt1), VT)) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Preservation-Pred-Succ-isNV-True'')).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![Vnv: vTerm, VT: vTy, Vtres: vTerm] : ((~(visNV(Vnv) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv)) & vptchecksimple(vPred(vt1), VT) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.41 tff(8,plain,(
% 0.20/0.41 ~((~(visNV(Vnv!64) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv!64)) & vptchecksimple(vPred(vt1), VT!63) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres!62)))) | vptchecksimple(Vtres!62, VT!63))),
% 0.20/0.41 inference(skolemize,[status(sab)],[7])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (visNV(Vnv!64) & (~(vt1 = vZero)) & (vt1 = vSucc(Vnv!64)) & vptchecksimple(vPred(vt1), VT!63) & (vreduce(vPred(vt1)) = vsomeTerm(Vtres!62))),
% 0.20/0.41 inference(or_elim,[status(thm)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (vt1 = vSucc(Vnv!64)),
% 0.20/0.41 inference(and_elim,[status(thm)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (vSucc(Vnv!64) = vt1),
% 0.20/0.41 inference(symmetry,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (vPred(vSucc(Vnv!64)) = vPred(vt1)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (vptchecksimple(vPred(vSucc(Vnv!64)), VT!63) <=> vptchecksimple(vPred(vt1), VT!63)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (vptchecksimple(vPred(vt1), VT!63) <=> vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)),
% 0.20/0.42 inference(symmetry,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (vptchecksimple(vPred(vt1), VT!63)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (^[Vt1: vTerm, VT: vTy] : refl(((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat)) <=> ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (^[Vt1: vTerm, VT: vTy] : rewrite((vptchecksimple(vPred(Vt1), VT) => (VT = vNat)) <=> ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : (vptchecksimple(vPred(Vt1), VT) => (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.42 tff(22,axiom,(![Vt1: vTerm, VT: vTy] : (vptchecksimple(vPred(Vt1), VT) => (VT = vNat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''TPred_inv2'')).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.42 tff(25,plain,(
% 0.20/0.42 ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(skolemize,[status(sab)],[24])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))) | ((~vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)) | (VT!63 = vNat))) <=> ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))) | (~vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)) | (VT!63 = vNat))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))) | ((~vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)) | (VT!63 = vNat))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vPred(Vt1), VT)) | (VT = vNat))) | (~vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)) | (VT!63 = vNat)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((~vptchecksimple(vPred(vSucc(Vnv!64)), VT!63)) | (VT!63 = vNat)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (VT!63 = vNat),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[30, 16])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (vNat = VT!63),
% 0.20/0.42 inference(symmetry,[status(thm)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt) <=> ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt) <=> ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,axiom,(![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''getTerm-0'')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,(
% 0.20/0.42 ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.20/0.42 inference(skolemize,[status(sab)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)) | (vgetTerm(vsomeTerm(Vtres!62)) = Vtres!62)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (vgetTerm(vsomeTerm(Vtres!62)) = Vtres!62),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (vreduce(vPred(vt1)) = vsomeTerm(Vtres!62)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (vreduce(vPred(vSucc(Vnv!64))) = vreduce(vPred(vt1))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (visNV(Vnv!64)),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (^[Vnv: vTerm] : refl(((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))) <=> ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))) <=> ![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))) <=> ![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[Vnv: vTerm] : rewrite((visNV(Vnv) => (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))) <=> ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![Vnv: vTerm] : (visNV(Vnv) => (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv))) <=> ![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,axiom,(![Vnv: vTerm] : (visNV(Vnv) => (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''reduce-7'')).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.42 tff(52,plain,(
% 0.20/0.42 ![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (((~![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))) | ((~visNV(Vnv!64)) | (vreduce(vPred(vSucc(Vnv!64))) = vsomeTerm(Vnv!64)))) <=> ((~![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))) | (~visNV(Vnv!64)) | (vreduce(vPred(vSucc(Vnv!64))) = vsomeTerm(Vnv!64)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))) | ((~visNV(Vnv!64)) | (vreduce(vPred(vSucc(Vnv!64))) = vsomeTerm(Vnv!64)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~![Vnv: vTerm] : ((~visNV(Vnv)) | (vreduce(vPred(vSucc(Vnv))) = vsomeTerm(Vnv)))) | (~visNV(Vnv!64)) | (vreduce(vPred(vSucc(Vnv!64))) = vsomeTerm(Vnv!64))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (vreduce(vPred(vSucc(Vnv!64))) = vsomeTerm(Vnv!64)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (vsomeTerm(Vnv!64) = vreduce(vPred(vSucc(Vnv!64)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[57])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (vsomeTerm(Vnv!64) = vsomeTerm(Vtres!62)),
% 0.20/0.42 inference(transitivity,[status(thm)],[58, 42, 41])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (vgetTerm(vsomeTerm(Vnv!64)) = vgetTerm(vsomeTerm(Vtres!62))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)) | (vgetTerm(vsomeTerm(Vnv!64)) = Vnv!64)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (vgetTerm(vsomeTerm(Vnv!64)) = Vnv!64),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 38])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (Vnv!64 = vgetTerm(vsomeTerm(Vnv!64))),
% 0.20/0.42 inference(symmetry,[status(thm)],[62])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (Vnv!64 = Vtres!62),
% 0.20/0.43 inference(transitivity,[status(thm)],[63, 60, 40])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (vptchecksimple(Vnv!64, vNat) <=> vptchecksimple(Vtres!62, VT!63)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[64, 32])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (vptchecksimple(Vtres!62, VT!63) <=> vptchecksimple(Vnv!64, vNat)),
% 0.20/0.43 inference(symmetry,[status(thm)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~vptchecksimple(Vtres!62, VT!63)) <=> (~vptchecksimple(Vnv!64, vNat))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (~vptchecksimple(Vtres!62, VT!63)),
% 0.20/0.43 inference(or_elim,[status(thm)],[8])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (~vptchecksimple(Vnv!64, vNat)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (^[Vt: vTerm] : refl(((~visNV(Vt)) | vptchecksimple(Vt, vNat)) <=> ((~visNV(Vt)) | vptchecksimple(Vt, vNat)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat)) <=> ![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat)) <=> ![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (^[Vt: vTerm] : rewrite((visNV(Vt) => vptchecksimple(Vt, vNat)) <=> ((~visNV(Vt)) | vptchecksimple(Vt, vNat)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![Vt: vTerm] : (visNV(Vt) => vptchecksimple(Vt, vNat)) <=> ![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.43 tff(75,axiom,(![Vt: vTerm] : (visNV(Vt) => vptchecksimple(Vt, vNat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','isNVisNat')).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.43 tff(78,plain,(
% 0.20/0.43 ![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(skolemize,[status(sab)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))) | ((~visNV(Vnv!64)) | vptchecksimple(Vnv!64, vNat))) <=> ((~![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))) | (~visNV(Vnv!64)) | vptchecksimple(Vnv!64, vNat))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))) | ((~visNV(Vnv!64)) | vptchecksimple(Vnv!64, vNat))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![Vt: vTerm] : ((~visNV(Vt)) | vptchecksimple(Vt, vNat))) | (~visNV(Vnv!64)) | vptchecksimple(Vnv!64, vNat)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (vptchecksimple(Vnv!64, vNat)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 79, 43])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[83, 69])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------