%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM226_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n031.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 0.19s 0.45s
% Output : Proof 0.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM226_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:11:10 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(vptchecksimple_type, type, (
% 0.19/0.45 vptchecksimple: ( vTerm * vTy ) > $o)).
% 0.19/0.45 tff(vNat_type, type, (
% 0.19/0.45 vNat: vTy)).
% 0.19/0.45 tff(tptp_fun_VwildcardName0_12_type, type, (
% 0.19/0.45 tptp_fun_VwildcardName0_12: vOptTerm > vTerm)).
% 0.19/0.45 tff(vreduce_type, type, (
% 0.19/0.45 vreduce: vTerm > vOptTerm)).
% 0.19/0.45 tff(vt1_type, type, (
% 0.19/0.45 vt1: vTerm)).
% 0.19/0.45 tff(vgetTerm_type, type, (
% 0.19/0.45 vgetTerm: vOptTerm > vTerm)).
% 0.19/0.45 tff(vsomeTerm_type, type, (
% 0.19/0.45 vsomeTerm: vTerm > vOptTerm)).
% 0.19/0.45 tff(visSomeTerm_type, type, (
% 0.19/0.45 visSomeTerm: vOptTerm > $o)).
% 0.19/0.45 tff(tptp_fun_Vtres_62_type, type, (
% 0.19/0.45 tptp_fun_Vtres_62: vTerm)).
% 0.19/0.45 tff(vSucc_type, type, (
% 0.19/0.45 vSucc: vTerm > vTerm)).
% 0.19/0.45 tff(tptp_fun_VT_63_type, type, (
% 0.19/0.45 tptp_fun_VT_63: vTy)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 ((~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))) <=> (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 ((~![VT: vTy, Vtres: vTerm] : (((visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT)) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))) <=> (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(3,axiom,(~![VT: vTy, Vtres: vTerm] : (((visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT)) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-Succ-isSomeTerm-True'')).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (~![VT: vTy, Vtres: vTerm] : ((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.45 tff(8,plain,(
% 0.19/0.45 ~((~(visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT!63) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres!62)))) | vptchecksimple(Vtres!62, VT!63))),
% 0.19/0.45 inference(skolemize,[status(sab)],[7])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (visSomeTerm(vreduce(vt1)) & vptchecksimple(vSucc(vt1), VT!63) & (vreduce(vSucc(vt1)) = vsomeTerm(Vtres!62))),
% 0.19/0.45 inference(or_elim,[status(thm)],[8])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (visSomeTerm(vreduce(vt1))),
% 0.19/0.45 inference(and_elim,[status(thm)],[9])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (^[VOptTerm0: vOptTerm] : refl(((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0)))) <=> ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0)))) <=> ![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0))) <=> ![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (^[VOptTerm0: vOptTerm] : rewrite((visSomeTerm(VOptTerm0) => ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0))) <=> ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : (visSomeTerm(VOptTerm0) => ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0))) <=> ![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.45 tff(16,axiom,(![VOptTerm0: vOptTerm] : (visSomeTerm(VOptTerm0) => ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''isSomeTerm-true-INV'')).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | ?[VwildcardName0: vTerm] : (VOptTerm0 = vsomeTerm(VwildcardName0)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.45 tff(19,plain,(
% 0.19/0.45 ![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[18])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (((~![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))) <=> ((~![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 ((~![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 ((~![VOptTerm0: vOptTerm] : ((~visSomeTerm(VOptTerm0)) | (VOptTerm0 = vsomeTerm(tptp_fun_VwildcardName0_12(VOptTerm0))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (vgetTerm(vreduce(vt1)) = vgetTerm(vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (vgetTerm(vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))) = vgetTerm(vreduce(vt1))),
% 0.19/0.45 inference(symmetry,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt) <=> ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt) <=> ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(29,axiom,(![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''getTerm-0'')).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.45 tff(31,plain,(
% 0.19/0.45 ![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.19/0.45 inference(skolemize,[status(sab)],[30])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((~![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)) | (vgetTerm(vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))) = tptp_fun_VwildcardName0_12(vreduce(vt1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (vgetTerm(vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))) = tptp_fun_VwildcardName0_12(vreduce(vt1))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (tptp_fun_VwildcardName0_12(vreduce(vt1)) = vgetTerm(vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))),
% 0.19/0.45 inference(symmetry,[status(thm)],[34])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (tptp_fun_VwildcardName0_12(vreduce(vt1)) = vgetTerm(vreduce(vt1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[35, 26])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) <=> vptchecksimple(vgetTerm(vreduce(vt1)), vNat)),
% 0.19/0.45 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (vptchecksimple(vgetTerm(vreduce(vt1)), vNat) <=> vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat)),
% 0.19/0.45 inference(symmetry,[status(thm)],[37])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 ((~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) <=> (~vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (vptchecksimple(vSucc(vt1), VT!63)),
% 0.19/0.45 inference(and_elim,[status(thm)],[9])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (^[Vt1: vTerm, VT: vTy] : refl(((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat)) <=> ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (^[Vt1: vTerm, VT: vTy] : rewrite((vptchecksimple(vSucc(Vt1), VT) => (VT = vNat)) <=> ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : (vptchecksimple(vSucc(Vt1), VT) => (VT = vNat)) <=> ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.45 tff(46,axiom,(![Vt1: vTerm, VT: vTy] : (vptchecksimple(vSucc(Vt1), VT) => (VT = vNat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''TSucc_inv1'')).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.45 tff(49,plain,(
% 0.19/0.45 ![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(skolemize,[status(sab)],[48])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))) | ((~vptchecksimple(vSucc(vt1), VT!63)) | (VT!63 = vNat))) <=> ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))) | (~vptchecksimple(vSucc(vt1), VT!63)) | (VT!63 = vNat))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))) | ((~vptchecksimple(vSucc(vt1), VT!63)) | (VT!63 = vNat))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 ((~![Vt1: vTerm, VT: vTy] : ((~vptchecksimple(vSucc(Vt1), VT)) | (VT = vNat))) | (~vptchecksimple(vSucc(vt1), VT!63)) | (VT!63 = vNat)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (VT!63 = vNat),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (vNat = VT!63),
% 0.19/0.45 inference(symmetry,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 ((~![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)) | (vgetTerm(vsomeTerm(Vtres!62)) = Vtres!62)),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (vgetTerm(vsomeTerm(Vtres!62)) = Vtres!62),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[56, 32])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (vreduce(vSucc(vt1)) = vsomeTerm(Vtres!62)),
% 0.19/0.45 inference(and_elim,[status(thm)],[9])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (vgetTerm(vreduce(vSucc(vt1))) = vgetTerm(vsomeTerm(Vtres!62))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (^[Vt1: vTerm] : refl(((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (^[Vt1: vTerm] : rewrite((visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (![Vt1: vTerm] : (visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1)))))) <=> ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.45 tff(66,axiom,(![Vt1: vTerm] : (visSomeTerm(vreduce(Vt1)) => (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''reduce-4'')).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.45 tff(69,plain,(
% 0.19/0.45 ![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[68])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.45 tff(71,plain,
% 0.19/0.45 (![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.19/0.45 tff(72,plain,
% 0.19/0.45 (((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))) <=> ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(73,plain,
% 0.19/0.45 ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | ((~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(74,plain,
% 0.19/0.45 ((~![Vt1: vTerm] : ((~visSomeTerm(vreduce(Vt1))) | (vreduce(vSucc(Vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(Vt1))))))) | (~visSomeTerm(vreduce(vt1))) | (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1)))))),
% 0.28/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.28/0.45 tff(75,plain,
% 0.28/0.45 (vreduce(vSucc(vt1)) = vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))),
% 0.28/0.45 inference(unit_resolution,[status(thm)],[74, 71, 10])).
% 0.28/0.45 tff(76,plain,
% 0.28/0.45 (vsomeTerm(vSucc(vgetTerm(vreduce(vt1)))) = vreduce(vSucc(vt1))),
% 0.28/0.45 inference(symmetry,[status(thm)],[75])).
% 0.28/0.45 tff(77,plain,
% 0.28/0.45 (vgetTerm(vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))) = vgetTerm(vreduce(vSucc(vt1)))),
% 0.28/0.45 inference(monotonicity,[status(thm)],[76])).
% 0.28/0.45 tff(78,plain,
% 0.28/0.45 ((~![Vt: vTerm] : (vgetTerm(vsomeTerm(Vt)) = Vt)) | (vgetTerm(vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))) = vSucc(vgetTerm(vreduce(vt1))))),
% 0.28/0.45 inference(quant_inst,[status(thm)],[])).
% 0.28/0.45 tff(79,plain,
% 0.28/0.45 (vgetTerm(vsomeTerm(vSucc(vgetTerm(vreduce(vt1))))) = vSucc(vgetTerm(vreduce(vt1)))),
% 0.28/0.45 inference(unit_resolution,[status(thm)],[78, 32])).
% 0.28/0.45 tff(80,plain,
% 0.28/0.45 (vSucc(vgetTerm(vreduce(vt1))) = vgetTerm(vsomeTerm(vSucc(vgetTerm(vreduce(vt1)))))),
% 0.28/0.45 inference(symmetry,[status(thm)],[79])).
% 0.28/0.45 tff(81,plain,
% 0.28/0.45 (vSucc(vgetTerm(vreduce(vt1))) = Vtres!62),
% 0.28/0.45 inference(transitivity,[status(thm)],[80, 77, 59, 57])).
% 0.28/0.45 tff(82,plain,
% 0.28/0.45 (vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat) <=> vptchecksimple(Vtres!62, VT!63)),
% 0.28/0.45 inference(monotonicity,[status(thm)],[81, 55])).
% 0.28/0.45 tff(83,plain,
% 0.28/0.45 (vptchecksimple(Vtres!62, VT!63) <=> vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat)),
% 0.28/0.45 inference(symmetry,[status(thm)],[82])).
% 0.28/0.45 tff(84,plain,
% 0.28/0.45 ((~vptchecksimple(Vtres!62, VT!63)) <=> (~vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat))),
% 0.28/0.45 inference(monotonicity,[status(thm)],[83])).
% 0.28/0.45 tff(85,plain,
% 0.28/0.45 (~vptchecksimple(Vtres!62, VT!63)),
% 0.28/0.45 inference(or_elim,[status(thm)],[8])).
% 0.28/0.45 tff(86,plain,
% 0.28/0.45 (~vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat)),
% 0.28/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.28/0.45 tff(87,plain,
% 0.28/0.45 (^[Vt1: vTerm] : refl(((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat)) <=> ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat)))),
% 0.28/0.45 inference(bind,[status(th)],[])).
% 0.28/0.45 tff(88,plain,
% 0.28/0.45 (![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(quant_intro,[status(thm)],[87])).
% 0.28/0.45 tff(89,plain,
% 0.28/0.45 (![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(rewrite,[status(thm)],[])).
% 0.28/0.45 tff(90,plain,
% 0.28/0.45 (^[Vt1: vTerm] : rewrite((vptchecksimple(Vt1, vNat) => vptchecksimple(vSucc(Vt1), vNat)) <=> ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat)))),
% 0.28/0.45 inference(bind,[status(th)],[])).
% 0.28/0.45 tff(91,plain,
% 0.28/0.45 (![Vt1: vTerm] : (vptchecksimple(Vt1, vNat) => vptchecksimple(vSucc(Vt1), vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.28/0.45 tff(92,axiom,(![Vt1: vTerm] : (vptchecksimple(Vt1, vNat) => vptchecksimple(vSucc(Vt1), vNat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''TSucc'')).
% 0.28/0.45 tff(93,plain,
% 0.28/0.45 (![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.28/0.45 tff(94,plain,
% 0.28/0.45 (![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.28/0.45 tff(95,plain,(
% 0.28/0.45 ![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(skolemize,[status(sab)],[94])).
% 0.28/0.45 tff(96,plain,
% 0.28/0.45 (![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))),
% 0.28/0.45 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.28/0.45 tff(97,plain,
% 0.28/0.45 (((~![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))) | ((~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) | vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat))) <=> ((~![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))) | (~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) | vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat))),
% 0.28/0.46 inference(rewrite,[status(thm)],[])).
% 0.28/0.46 tff(98,plain,
% 0.28/0.46 ((~![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))) | ((~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) | vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat))),
% 0.28/0.46 inference(quant_inst,[status(thm)],[])).
% 0.28/0.46 tff(99,plain,
% 0.28/0.46 ((~![Vt1: vTerm] : ((~vptchecksimple(Vt1, vNat)) | vptchecksimple(vSucc(Vt1), vNat))) | (~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) | vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat)),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.28/0.46 tff(100,plain,
% 0.28/0.46 ((~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)) | vptchecksimple(vSucc(vgetTerm(vreduce(vt1))), vNat)),
% 0.28/0.46 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.28/0.46 tff(101,plain,
% 0.28/0.46 (~vptchecksimple(vgetTerm(vreduce(vt1)), vNat)),
% 0.28/0.46 inference(unit_resolution,[status(thm)],[100, 86])).
% 0.28/0.46 tff(102,plain,
% 0.28/0.46 (~vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat)),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[101, 39])).
% 0.28/0.46 tff(103,plain,
% 0.28/0.46 (vptchecksimple(vSucc(vt1), VT!63) <=> vptchecksimple(vSucc(vt1), vNat)),
% 0.28/0.46 inference(monotonicity,[status(thm)],[54])).
% 0.28/0.46 tff(104,plain,
% 0.28/0.46 (vptchecksimple(vSucc(vt1), vNat)),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[40, 103])).
% 0.28/0.46 tff(105,plain,
% 0.28/0.46 (^[Vt1: vTerm] : refl(((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat)) <=> ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat)))),
% 0.28/0.46 inference(bind,[status(th)],[])).
% 0.28/0.46 tff(106,plain,
% 0.28/0.46 (![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.28/0.46 tff(107,plain,
% 0.28/0.46 (![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(rewrite,[status(thm)],[])).
% 0.28/0.46 tff(108,plain,
% 0.28/0.46 (^[Vt1: vTerm] : rewrite((vptchecksimple(vSucc(Vt1), vNat) => vptchecksimple(Vt1, vNat)) <=> ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat)))),
% 0.28/0.46 inference(bind,[status(th)],[])).
% 0.28/0.46 tff(109,plain,
% 0.28/0.46 (![Vt1: vTerm] : (vptchecksimple(vSucc(Vt1), vNat) => vptchecksimple(Vt1, vNat)) <=> ![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(quant_intro,[status(thm)],[108])).
% 0.28/0.46 tff(110,axiom,(![Vt1: vTerm] : (vptchecksimple(vSucc(Vt1), vNat) => vptchecksimple(Vt1, vNat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''TSucc_inv2'')).
% 0.28/0.46 tff(111,plain,
% 0.28/0.46 (![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.28/0.46 tff(112,plain,
% 0.28/0.46 (![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.28/0.46 tff(113,plain,(
% 0.28/0.46 ![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(skolemize,[status(sab)],[112])).
% 0.28/0.46 tff(114,plain,
% 0.28/0.46 (![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.28/0.46 tff(115,plain,
% 0.28/0.46 (((~![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))) | ((~vptchecksimple(vSucc(vt1), vNat)) | vptchecksimple(vt1, vNat))) <=> ((~![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))) | (~vptchecksimple(vSucc(vt1), vNat)) | vptchecksimple(vt1, vNat))),
% 0.28/0.46 inference(rewrite,[status(thm)],[])).
% 0.28/0.46 tff(116,plain,
% 0.28/0.46 ((~![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))) | ((~vptchecksimple(vSucc(vt1), vNat)) | vptchecksimple(vt1, vNat))),
% 0.28/0.46 inference(quant_inst,[status(thm)],[])).
% 0.28/0.46 tff(117,plain,
% 0.28/0.46 ((~![Vt1: vTerm] : ((~vptchecksimple(vSucc(Vt1), vNat)) | vptchecksimple(Vt1, vNat))) | (~vptchecksimple(vSucc(vt1), vNat)) | vptchecksimple(vt1, vNat)),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.28/0.46 tff(118,plain,
% 0.28/0.46 ((~vptchecksimple(vSucc(vt1), vNat)) | vptchecksimple(vt1, vNat)),
% 0.28/0.46 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.28/0.46 tff(119,plain,
% 0.28/0.46 (vptchecksimple(vt1, vNat)),
% 0.28/0.46 inference(unit_resolution,[status(thm)],[118, 104])).
% 0.28/0.46 tff(120,plain,
% 0.28/0.46 (^[VT: vTy, Vtres: vTerm] : refl((vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))) <=> (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))))),
% 0.28/0.46 inference(bind,[status(th)],[])).
% 0.28/0.46 tff(121,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))) <=> ![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))),
% 0.28/0.46 inference(quant_intro,[status(thm)],[120])).
% 0.28/0.46 tff(122,plain,
% 0.28/0.46 (^[VT: vTy, Vtres: vTerm] : trans(monotonicity(trans(monotonicity(rewrite((vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres))) <=> (~((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))))), ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) <=> (~(~((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))))))), rewrite((~(~((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))))) <=> ((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))), ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) <=> ((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))))), (((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)) <=> (((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))), rewrite((((~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)) <=> (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))), (((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)) <=> (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))))),
% 0.28/0.46 inference(bind,[status(th)],[])).
% 0.28/0.46 tff(123,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)) <=> ![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))),
% 0.28/0.46 inference(quant_intro,[status(thm)],[122])).
% 0.28/0.46 tff(124,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)) <=> ![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.28/0.46 inference(rewrite,[status(thm)],[])).
% 0.28/0.46 tff(125,plain,
% 0.28/0.46 (^[VT: vTy, Vtres: vTerm] : rewrite(((vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT)) <=> ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT)))),
% 0.28/0.46 inference(bind,[status(th)],[])).
% 0.28/0.46 tff(126,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : ((vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT)) <=> ![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.28/0.46 inference(quant_intro,[status(thm)],[125])).
% 0.28/0.46 tff(127,axiom,(![VT: vTy, Vtres: vTerm] : ((vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres))) => vptchecksimple(Vtres, VT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Preservation-Succ-IH0'')).
% 0.28/0.46 tff(128,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.28/0.46 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.28/0.46 tff(129,plain,
% 0.28/0.46 (![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.28/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.28/0.47 tff(130,plain,(
% 0.28/0.47 ![VT: vTy, Vtres: vTerm] : ((~(vptchecksimple(vt1, VT) & (vreduce(vt1) = vsomeTerm(Vtres)))) | vptchecksimple(Vtres, VT))),
% 0.28/0.47 inference(skolemize,[status(sab)],[129])).
% 0.28/0.47 tff(131,plain,
% 0.28/0.47 (![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))),
% 0.28/0.47 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.28/0.47 tff(132,plain,
% 0.28/0.47 (![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))),
% 0.28/0.47 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.28/0.47 tff(133,plain,
% 0.28/0.47 (((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | ((~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))) <=> ((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))),
% 0.28/0.47 inference(rewrite,[status(thm)],[])).
% 0.28/0.47 tff(134,plain,
% 0.28/0.47 ((vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~vptchecksimple(vt1, vNat)) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))) <=> ((~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))),
% 0.28/0.47 inference(rewrite,[status(thm)],[])).
% 0.28/0.47 tff(135,plain,
% 0.28/0.47 (((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~vptchecksimple(vt1, vNat)) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))) <=> ((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | ((~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))))),
% 0.28/0.47 inference(monotonicity,[status(thm)],[134])).
% 0.28/0.47 tff(136,plain,
% 0.28/0.47 (((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~vptchecksimple(vt1, vNat)) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))) <=> ((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))),
% 0.28/0.47 inference(transitivity,[status(thm)],[135, 133])).
% 0.28/0.47 tff(137,plain,
% 0.28/0.47 ((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~vptchecksimple(vt1, vNat)) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1))))))),
% 0.28/0.47 inference(quant_inst,[status(thm)],[])).
% 0.28/0.47 tff(138,plain,
% 0.28/0.47 ((~![VT: vTy, Vtres: vTerm] : (vptchecksimple(Vtres, VT) | (~vptchecksimple(vt1, VT)) | (~(vreduce(vt1) = vsomeTerm(Vtres))))) | (~vptchecksimple(vt1, vNat)) | vptchecksimple(tptp_fun_VwildcardName0_12(vreduce(vt1)), vNat) | (~(vreduce(vt1) = vsomeTerm(tptp_fun_VwildcardName0_12(vreduce(vt1)))))),
% 0.28/0.47 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.28/0.47 tff(139,plain,
% 0.28/0.47 ($false),
% 0.28/0.47 inference(unit_resolution,[status(thm)],[138, 132, 119, 24, 102])).
% 0.28/0.47 % SZS output end Proof
% 0.28/0.47 % E exiting
%------------------------------------------------------------------------------